1. Topology History Topological ideas, concepts and functional analysis. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Topology_in_mathematics.h

A history of Topology Geometry and topology index History Topics Index Version for printing Topological ideas are present in almost all areas of today's mathematics. The subject of topology itself consists of several different branches, such as point set topology, algebraic topology and differential topology, which have relatively little in common. We shall trace the rise of topological concepts in a number of different situations. Perhaps the first work which deserves to be considered as the beginnings of topology is due to Euler . In 1736 Euler published a paper on the solution of the entitled Solutio problematis ad geometriam situs pertinentis which translates into English as The solution of a problem relating to the geometry of position. The title itself indicates that Euler was aware that he was dealing with a different type of geometry where distance was not relevant. Here is The paper not only shows that the problem of crossing the seven bridges in a single journey is impossible, but generalises the problem to show that, in today's notation, A graph has a path traversing each edge exactly once if exactly two vertices have odd degree.

2. Allen Hatcher's Homepage Links to online texts and papers (published and unpublished) on Algebraic topology, KTheory, and 3-Manifolds. http://www.math.cornell.edu/~hatcher/

Allen Hatcher Office: 553 Malott Hall Phone: (607)-255-4091 Book Projects: Algebraic Topology Vector Bundles and K-Theory Spectral Sequences in Algebraic Topology ... Topology of Numbers Course Notes: Basic 3-Manifold Topology Introductory Point-Set Topology Papers Other Things: Pictures of stable homotopy groups of spheres Pictures of the cohomology of SO(n) List of recommended books in Topology (from 2003, needs updating) Books by other authors Book Projects Algebraic Topology This is the first in a planned series of three textbooks in algebraic topology having the goal of covering all the basics while remaining readable by newcomers seeing the subject for the first time. The first book contains the basic core material along with a number of optional topics of a relatively elementary nature. The second and third books are only partially written - see below. To find out more about the first book or to download it in electronic form, follow this link to the download page Vector Bundles and K-Theory The intention is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. For further information, and to download the part of the book that is written, go to

3. Topology - Wikipedia, The Free Encyclopedia topology (from the Greek τόπος, “place”, and λόγος, “study”) is a major area of mathematics concerned with spatial properties that are preserved under http://en.wikipedia.org/wiki/Topology

Topology From Wikipedia, the free encyclopedia Jump to: navigation search This article includes a list of references , related reading or external links , but its sources remain unclear because it lacks inline citations Please improve this article by introducing more precise citations where appropriate (November 2009) Not to be confused with topography For other uses, see Topology (disambiguation) A Möbius strip , an object with only one surface and one edge. Such shapes are an object of study in topology. Topology (from the Greek τόπος, “place”, and λόγος, “study”) is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example, deformations that involve stretching, but no tearing or gluing. It emerged through the development of concepts from geometry and set theory , such as space, dimension, and transformation. Ideas that are now classified as topological were expressed as early as 1736. Toward the end of the 19th century, a distinct discipline developed, which was referred to in Latin as the geometria situs (“geometry of place”) or analysis situs (Greek-Latin for “picking apart of place”). This later acquired the modern name of topology. By the middle of the 20

4. Topology Glossary Definitions of over 100 terms in topology. http://www.ornl.gov/sci/ortep/topology/defs.txt

5. Network Topology - Wikipedia, The Free Encyclopedia Network topology is the layout pattern of interconnections of the various elements (links, nodes, etc.) of a computer network Network topologies may be physical or logical. http://en.wikipedia.org/wiki/Network_topology

Network topology From Wikipedia, the free encyclopedia Jump to: navigation search This article has multiple issues. Please help improve it or discuss these issues on the talk page It needs additional references or sources for verification Tagged since October 2008. It appears to contradict itself. Tagged since May 2009. It may need reorganization to meet Wikipedia's quality standards Tagged since May 2009. It may be confusing or unclear for some readers. Tagged since May 2009. It is in need of attention from an expert on the subject. Tagged since March 2010. It may need a complete rewrite to meet Wikipedia's quality standards Tagged since May 2009. Diagram of different network topologies. Network topology is the layout pattern of interconnections of the various elements ( links nodes , etc.) of a computer network Network topologies may be physical or logical. Physical topology means the physical design of a network including the devices, location and cable installation. Logical topology refers to how data is actually transferred in a network as opposed to its physical design. Topology can be considered as a virtual shape or structure of a network. This shape does not correspond to the actual physical design of the devices on the computer network. The computers on a home network can be arranged in a circle but it does not necessarily mean that it represents a ring topology.

6. ScienceDirect - Topology, Volume 48, Issues 2-4, Pages 41-224 (June-December 200 The online version of topology on ScienceDirect, the world's leading platform for high quality peerreviewed full-text publications in science, technology and health. http://www.sciencedirect.com/science/journal/00409383

Hub ScienceDirect Scopus Register ... Go to SciVal Suite Username: Password: Remember me Not Registered? Forgotten your username or password? Go to Athens / Institution login Home ... Help All fields Author Advanced search Journal/Book title Volume Issue Page Search tips Topology Sample Issue Online About this Journal Submit your Article Shortcut link to this Title ... New Article Feed Signed up for new Volumes / Issues [ remove Alert me about new Volumes / Issues Your selection(s) could not be saved due to an internal error. Please try again. Added to Favorites [ remove Add to Favorites Font Size: Add to my Quick Links Volume 48, Issues 2-4, Pages 41-224 (June-December 2009) SPECIAL ISSUE: Proceedings of the Infinite Dimensional Analysis and Topology (IDAT) Conference 2009 Edited by Richard M. Aron, Pablo Galindo, Andriy Zagorodnyuk and Mykhailo Zarichnyi = Full-text available = Abstract only Articles in Press Volumes 41 - 48 (2002 - 2009) Volume 48, Issues 2-4 - selected pp. 41-224 (June-December 2009)

7. Topology: Definition From Answers.com n. , pl. , gies . Topographic study of a given place, especially the history of a region as indicated by its topography. Medicine . The anatomical structure of a specific http://www.answers.com/topic/network-topology

8. Algebraic Topology -- From Wolfram MathWorld Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that http://mathworld.wolfram.com/AlgebraicTopology.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Derwent Algebraic Topology Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces spheres tori circles ... links , configuration spaces, etc.) that remain invariant under both-directions continuous one-to-one homeomorphic ) transformations. The discipline of algebraic topology is popularly known as "rubber-sheet geometry" and can also be viewed as the study of disconnectivities . Algebraic topology has a great deal of mathematical machinery for studying different kinds of hole structures, and it gets the prefix "algebraic" since many hole structures are represented best by algebraic objects like groups and rings Algebraic topology originated with combinatorial topology , but went beyond it probably for the first time in the 1930s when was developed. A technical way of saying this is that algebraic topology is concerned with functors from the topological category of groups and homomorphisms . Here, the

9. Algebraic General Topology And Math Synthesis - Replacement Of Mathematical Anal Abstract topological objects expressing infinities with algebraic operations. http://www.mathematics21.org/algebraic-general-topology.html

My homepage My math page My math news Donate for the research Algebraic General Topology and Math Synthesis I discovered Algebraic General Topology AGT ), a new field of math which will replace old General Topology. Mathematical Synthesis is how I call Algebraic General Topology applied to study of Mathematical Analysis. Please nominate me for Abel Prize. Please collaborate writing Filters on posets and generalization math book. AGT articles Funcoids and Reloids (PDF, draft) Consider generalizations of proximity spaces and uniform spaces. Also in this article continuity is defined algebraically hiding old epsilon-delta notion under a smart algebra. Generalizes continuousness, uniform continuousness, and proximity-continuousness in one formula. Convergence of funcoids (PDF, partial draft) Defined the notion of convergence and limit for funcoids. Defined (generalized) limit of arbitrary (not necessarily continuous) functions under certain conditions. Connectors and generalized connectedness (PDF, preprint) Defined the notion of connectedness for special binary relations called connectors. This generalizes topological connectedness, path connectedness, connectedness of digraphs, proximal connectedness, and some other kinds of connectedness.

10. Topology -- From Wolfram MathWorld topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle http://mathworld.wolfram.com/Topology.html

11. Publishing The Lync Server 2010 Enterprise Edition Topology Fails When The Centr Oct 28, 2010 Publishing the Lync Server 2010 Enterprise Edition topology fails when the Central Management Store is created http://support.microsoft.com/kb/2422384

12. General Topology At AllExperts Branch of topology which studies elementary properties. http://en.allexperts.com/e/g/ge/general_topology.htm

zDO=zis=1;zpid=zi=zRf=ztp=zpo=0;zdx=20;zfx=100;zJs=13 zi=1;zz='46860=1-1-1150;125125=2-1-12-1;120600=2-1-1250;11=1-1-1150;336280=2-1-1299;72890=2-1-1150';zx='3-1-1';zde=15;zdp=1440;zds=43200;zfp=0;zfs=0;zfd=100;zdd=20;zpb='';zhc='';zDO=1;zGR="ca-about-site_js";if(!this.zGL)zGL=5;zGTH=1;zAS=1 zGH="general topology history scope standard areas branches isbn spaces topological";zObT="General topology";zRad=5 zGRH=1 zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') zDO=0 AllExperts Encyclopedia Search General topology: Encyclopedia BETA Free Encyclopedia Index ... Questions and Answers zmhp('style="color:#fff"') Encyclopedia Contents History Scope See also Standard references ... License Free Online Courses 12 Weeks to Weight Loss Take Charge of Stress Learn How to Bake Budgeting 101 ... Misc General topology In mathematics general topology or point-set topology is the branch of topology which studies properties of topological space s and structures defined on them. It is distinct from other branches of topology in that the topological spaces may be very general, and do not have to be at all similar to manifold s.

13. Topology - Wikibooks, Collection Of Open-content Textbooks General topology is based solely on set theory and concerns itself with structures of sets. It is at its core a generalization of the concept of distance, though this will not http://en.wikibooks.org/wiki/Topology

Topology From Wikibooks, the open-content textbooks collection Jump to: navigation search This book contains mathematical formulae that look better rendered as PNG General Topology is based solely on set theory and concerns itself with structures of sets. It is at its core a generalization of the concept of distance, though this will not be immediately apparent for the novice student. Topology generalizes many distance-related concepts, such as continuity, compactness, and convergence. For an overview of the subject of topology, please see the Wikipedia entry Contents Before You Begin Point - Set Topology Some Set Theory Introduction to Topology ... edit Before You Begin In order to make things easier for you as a reader, as well as for the writers, you will be expected to be familiar with a few topics before beginning. Real analysis Continuous Functions Set Theory Set Operations: Union, Intersection, Complement, De Morgan's laws , etc. Order Relations : Ordered Sets, Equivalence relations, Lattices Functions: Definition and Properties of Functions Cardinality : Finite, Countable, and Uncountable sets

14. Topology This page was developed as an exercise in developing web pages in the frame of a course work in ISP53. http://www.albany.edu/~ap0349/isp523/web1/topology.html

Topology of Networking Topology A network can be arranged or configured in several different ways. Two types of topology is recognized: Physical Topology The physical topology of a network refers to configuration of cables, computers, and other peripherals. Logical Topology The logical topology is concerned with data transmission on the network,that is the methods used to pass information between workstations. Thus, the logical topology refers to data transmission protocols. The following are the four basic types of physical topology used in networks: Linear Bus Star Star-Wired Ring Tree Linear Bus All the communications travel along a common cable called a bus.A linear bus topology consists of a main run of a cable with a terminator at each end of the line. All nodes (file server, workstations, and peripherals) are connected to the linear cable. As the information passes along the bus, it is examined by each device to see if the information is intended for it. The bus network is typically used when only a few microcomputers are to be linked together. A twisted pair, coaxial or fiber optic cable can be used in this configuration. The protocols used with Linear Bus topology are Ethernet or LocalTalk. Advantages of a Linear Bus Topology: - Easy to connect a computer or peripheral to a linear bus.

15. Algebraic Topology - Wikipedia, The Free Encyclopedia An encyclopedic reference containing definitions, some discussion, and an assortment of useful links to various resources concerning Algebraic topology and K-Theory. http://en.wikipedia.org/wiki/Algebraic_topology

Algebraic topology From Wikipedia, the free encyclopedia Jump to: navigation search For the topology of pointwise convergence, see Algebraic topology (object) Algebraic topology is a branch of mathematics which uses tools from abstract algebra to study topological spaces . The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism , though usually most classify up to homotopy equivalence Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Contents The method of algebraic invariants Setting in category theory Results on homology Applications of algebraic topology ... edit The method of algebraic invariants An older name for the subject was combinatorial topology , implying an emphasis on how a space X was constructed from simpler ones (the modern standard tool for such construction is the CW-complex ). The basic method now applied in algebraic topology is to investigate spaces via algebraic invariants by mapping them, for example, to

16. Topology > Home topology is assisted by the Commonwealth Government through the Australia Council its arts funding and advisory body and by the Queensland Government through Arts Queensland. http://www.topologymusic.com/

Home About Us Discography Workshops ... Contact Sunday 14 November 6.00pm TEN HANDS Visy Theatre Brisbane Powerhouse Latest Blog Post From our hectic few days in Jakarta, I’ll keep with me…. Mon, 18 Oct 2010 05:17:00 +1100 Therese Milanovic, pianist's  fond memories of the kindness Tops encountered. More... Healthy album launch / concert Thu, 11 Mar 2010 06:18:00 +1100 Eight of Australia's most creative musicians together to give a live rendition of their new collaboration - Healthy, an album of original music that doesn't shy away from either knotty structures or direct emotion. More... Recent Press Queensland Symphony Orchestra Partnership Mon, 18 Oct 2010 04:30:48 +1100 TimeOff REVIEW: Bounce for the Brisbane Festival Mon, 27 Sep 2010 04:13:03 +1000 Live Reviews QUT FESTIVAL THEATRE, BRISBANE POWERHOUSE: 17.09.10 Despite representing a confluence of some of their city’s most technically accomplished instrumentalists and composers, Brisbane post-classical quintet, Topology have somehow always managed to cater to audiences with no specific interest in modern chamber music. It isn’t until one sees a boundary-blurring performance like tonight’s that one understands how the group has managed to acquire such a unique following. 'Healthy' Brisbane show and CD review Sat, 10 Jul 2010 14:00:00 +1000

17. Topology - Definition And More From The Free Merriam-Webster Dictionary Definition of word from the MerriamWebster Online Dictionary with audio pronunciations, thesaurus, Word of the Day, and word games. http://mw4.m-w.com/dictionary/topology

18. Crystallographic Topology The topology of Crystallographic Groups and Simple Crystal Structures http://www.ornl.gov/sci/ortep/topology.html

Crystallographic Topology The Topology of Crystallographic Groups and Simple Crystal Structures Carroll K. Johnson Michael N. Burnett Oak Ridge National Laboratory Australian Mirror Site UK Mirror Site Preprints and Presentations Crystallographic Topology 101 - A Tutorial / Virtual Course 1. Overview 2. Introduction to Orbifolds 2.1. Elliptic 2-Orbifolds from Point Groups 2.2. Euclidean 2-Orbifolds from Plane Groups 3. Introduction to Critical Nets 4. Critical Nets on Orbifolds ... Orbifold Atlas under construction Cubic Space Group Orbifolds What's New (Mar. 15, 1999) Colleagues and Their Abstracts Related Web Sites ... ORTEP-III Computer Program Send comments, questions, suggestions, etc. to: topology@ornl.gov Oak Ridge National Laboratory Home Page Page last revised:

19. What Is Topology? - A Word Definition From The Webopedia Computer Dictionary This page describes the term topology and lists other pages on the Web where you can find additional information. http://www.webopedia.com/TERM/T/topology.html

Webopedia.com Sign Up Sign In Search Term of the Day Recent Terms Did You Know? Quick Reference ... Home > topology topology )The shape of a local-area network (LAN) or other communications system. Topologies are either physical or logical There are four principal topologies used in LANs. bus topology: All devices are connected to a central cable, called the bus or backbone . Bus networks are relatively inexpensive and easy to install for small networks. Ethernet systems use a bus topology. ring topology All devices are connected to one another in the shape of a closed loop, so that each device is connected directly to two other devices, one on either side of it. Ring topologies are relatively expensive and difficult to install, but they offer high bandwidth and can span large distances. star topology: All devices are connected to a central hub . Star networks are relatively easy to install and manage, but bottlenecks can occur because all data must pass through the hub. tree topology: A tree topology combines characteristics of linear bus and star topologies. It consists of groups of star-configured workstations connected to a linear bus backbone cable. These topologies can also be mixed. For example, a bus-star network consists of a high-bandwidth bus, called the

20. Topological Properties Topological Properties of Quaternions Topological space Open sets Hausdorff topology Compact sets R^1 versus R^n (section under development) Topological Space http://www.theworld.com/~sweetser/quaternions/intro/topology/topology.html

Topological Properties of Quaternions Topological space Open sets Hausdorff topology Compact sets ... R^1 versus R^n (section under development) Topological Space If we choose to work systematically through Wald's "General Relativity", the starting point is "Appendix A, Topological Spaces". Roughly, topology is the structure of relationships that do not change if a space is distorted. Some of the results of topology are required to make calculus rigorous. In this section, I will work consistently with the set of quaternions, H^1, or just H for short. The difference between the real numbers R and H is that H is not a totally ordered set and multiplication is not commutative. These differences are not important for basic topological properties, so statements and proofs involving H are often identical to those for R. First an open ball of quaternions needs to be defined to set the stage for an open set. Define an open ball in H of radius (r, 0) centered around a point (y, Y) [note: small letters are scalars, capital letters are 3-vectors] consisting of points (x, X) such that An open set in H is any set which can be expressed as a union of open balls.

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