1. General Topology - Wikipedia, The Free Encyclopedia In mathematics, general topology or pointset topology is the branch of topology which studies properties of topological spaces and structures defined on http://en.wikipedia.org/wiki/General_topology

General topology From Wikipedia, the free encyclopedia Jump to: navigation search Please help improve this article by expanding it. Further information might be found on the talk page (August 2009) In mathematics general topology or point-set topology is the branch of topology which studies properties of topological spaces 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 manifolds Contents Definition History Scope See also ... edit Definition A topology is a pair ( X ,Σ) consisting of a set X and a collection Σ of subsets of X , called open sets, satisfying the following three axioms The union of open sets is an open set. The finite intersection of open sets is an open set. X and the empty set ∅ are open sets. edit History General topology grew out of a number of areas, most importantly the following: the detailed study of subsets of the real line (once known as the topology of point sets , this usage is now obsolete) the introduction of the manifold concept the study of metric spaces , esp.

2. General Topology In mathematics, general topology or pointset topology is the branch of topology which studies properties of topological spaces and structures defined on them http://pediaview.com/openpedia/General_topology

General topology In mathematics general topology or point-set topology is the branch of topology which studies properties of topological spaces 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 manifolds Contents Definition History Scope See also ... References Definition A topology is a pair ( X ,Σ) consisting of a set X and a collection Σ of subsets of X , called open sets, satisfying the following three axioms The union of open sets is an open set. The finite intersection of open sets is an open set. X and the empty set ∅ are open sets. History General topology grew out of a number of areas, most importantly the following: the detailed study of subsets of the real line (once known as the topology of point sets , this usage is now obsolete) the introduction of the manifold concept the study of metric spaces , esp. normed linear spaces , in the early days of functional analysis General topology assumed its present form around 1940. It captures, one might say, almost everything in the intuition of continuity , in a technically adequate form that can be applied in any area of mathematics.

3. 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.

4. General Topology - Slider In mathematics, general topology or point set topology is the branch of topology which studies elementary properties of topological spaces and structures defined on them. http://enc.slider.com/Enc/General_topology

Advanced Help Encyclopedia Directory Encyclopaedia G Ge Gea ... Gez General topology In mathematics general topology or point set topology is the branch of topology which studies elementary properties of topological spaces and structures defined on them. It grew out of a number of areas, such as the detailed study of sets of points (as subsets of the real line , understood), the manifold concept, the metric spaces and the early days of functional analysis . It was codified, in much its form for the remainder of the twentieth century , around 1940. It captures, one might say, almost everything in the intuition of continuity , in a technically adequate form that can be applied in every area of mathematics. More specifically, it is in general topology that basic notions, such as: open and closed sets interior and exterior neighbourhood and closeness compact spaces continuous functions ... convergence of sequences nets , and filters separation axioms are defined and theorems about them are proved. Other more advanced notions also appear, but are usually related directly to these fundamental concepts, without reference to other branches of mathematics. Other main branches of topology are algebraic topology geometric topology , and differential topology . As the name implies, general topology provides the common foundation for these areas.

5. General Topology A selection of articles related to General Topology general topology Encyclopedia Areas of mathematics. The aim of this page is to list all areas of modern mathematics, with a http://www.experiencefestival.com/general_topology

6. Category:General Topology - Wikipedia, The Free Encyclopedia The main article for this category is General topology. In mathematics, general topology or point set topology is that branch of topology which studies properties of general http://en.wikipedia.org/wiki/Category:General_topology

Category:General topology From Wikipedia, the free encyclopedia Jump to: navigation search The main article for this category is General topology In mathematics general topology or point set topology is that branch of topology which studies properties of general topological spaces (which may not have further structure; for example, they may not be manifolds ), and structures defined on them. Subcategories This category has the following 8 subcategories, out of 8 total. C Closure operators (2 C, 27 P) Continuum theory (6 P) D Digital topology (4 P) D cont. Dimension theory (19 P) S Separation axioms (17 P) T Topological games (2 P) T cont. Topological vector spaces (2 C, 30 P) Topology of function spaces (1 C, 21 P) Pages in category "General topology" The following 139 pages are in this category, out of 139 total. This list may not reflect recent changes ( learn more Glossary of topology List of general topology topics General topology A Adherent point Alexandroff extension Appert topology Axiom of countability B Baire category theorem Baire function Baire set Baire space ... Boundary (topology) C Category of topological spaces Cauchy space Characterizations of the category of topological spaces Clopen set ... Cylinder set D Dante space Dense set Derived set (mathematics) Development (topology) ... Disjoint union (topology) D cont.

7. General Topology By The SwissPedia, The Free Encyclopedia By Just Click Search General topology. The biggest multilingual freecontent encyclopedia on the Internet. Over 7 million articles in over 200 languages, and still growing. http://www.swisscorner.com/wiki.php?title=General_topology

8. Math.com Store: Math Books: General Topology General Topology Textbook Buyback - Math Books - Math.com Store the best place to shop for math supplies. http://store.math.com/Books-1000-0486434796-General_Topology.html

9. General Topology At AllExperts In mathematics general topology or pointset topology is the branch of topology which studies properties of topological space s and structures defined on them It is distinct from http://www.associatepublisher.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.

10. General Topology | TripAtlas.com In mathematics, general topology or pointset topology is the branch of topology which studies properties of topological spaces and structures defined on them. It is distinct http://tripatlas.com/General_topology

11. General Topology In Encyclopedia General topology in Encyclopedia in Encyclopedia http://www.tutorgig.com/ed/General_topology

12. Math.com Store: Math Books: General Topology General Topology Textbook Buyback - Math Books - Math.com Store the best place to shop for math supplies. http://store.math.com/Books-1000-0923891552-General_Topology.html

13. General Topology - Definition In mathematics, general topology or point set topology is that branch of topology which studies elementary properties of topological spaces and structures defined on them. http://www.wordiq.com/definition/General_topology

General topology - Definition In mathematics general topology or point set topology is that branch of topology which studies elementary properties of topological spaces and structures defined on them. It grew out of a number of areas, such as the detailed study of sets of points (as subsets of the real line , understood), the manifold concept, the metric spaces and the early days of functional analysis . It was codified, in much its form for the remainder of the twentieth century , around 1940. It captures, one might say, almost everything in the intuition of continuity , in a technically adequate form that can be applied in every area of mathematics. More specifically, it is in general topology that basic notions, such as: open and closed sets compact spaces continuous functions ... convergence of sequences nets , and filters separation axioms are defined and theorems about them are proved. Other more advanced notions also appear, but are usually related directly to these fundamental concepts, without reference to other branches of mathematics. Other main branches of topology are algebraic topology geometric topology , and differential topology . As the name implies, general topology provides the common foundation for these areas.

14. General Topology Topics At Duck Duck Go Alexandroff extension In mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way http://duckduckgo.com/c/General_topology

15. General Topology - Discussion And Encyclopedia Article. Who Is General Topology? General topology. Discussion about General topology. Ecyclopedia or dictionary article about General topology. http://www.knowledgerush.com/kr/encyclopedia/General_topology/

16. Algebraic General Topology - Wikinfo Algebraic general topology (AGT) is the theory of funcoids and reloids. It is called algebraic because there are algebraic operations on the sets of funcoids and reloids. http://www.wikinfo.org/index.php/Algebraic_general_topology

Algebraic general topology From Wikinfo Jump to: navigation search Algebraic general topology (AGT) is the theory of funcoids and reloids It is called algebraic because there are algebraic operations on the sets of funcoids and reloids. For example (generalized) continuousness is defined with algebraic formulas instead of bad old epsilon-delta notation. (See Algebraic General Topology for details.) AGT as new field of research During decades the development of general topology was stalled. It was said that general topology is dead meaning that nothing significantly new can be discovered in this field. Introduction of AGT revolutionaries general topology with a new field of research. At the time of writing this there are more than 17 open problems about funcoids and reloids , see Open Problem Garden Victor Porton pleads to nominate him for Abel Prize for the discovery of AGT. External links Algebraic General Topology Retrieved from " http://www.wikinfo.org/index.php/Algebraic_general_topology Category Mathematics Views Page Discussion View source History Personal tools Log in / create account Navigation Main Page Community portal Current events Contents ... Donate Search Toolbox What links here Related changes Special pages Printable version ... Permanent link This page was last modified on 11 November 2008, at 19:03.

17. KU Department Of Mathematics : General Topology Departmental website for the University of Kansas Department of Mathematics. http://www.math.ku.edu/research/research-areas/research-general_topology.html

KU Home Math Home Math Webmail Kyou Department of Mathematics People Faculty/Lecturers Students Administration Academics Graduate Admissions Degrees Courses ... Scholarships Research Research Areas Algebra Analysis Combinatorics ... KUMUNU Additional information Current Students Student Organizations Prospective Students Visitors ... Sample Problems General Topology William Fleissner Charles Himmelberg Jack Porter Judith Roitman ... Contact KU

18. General Topology | The Jewish Week Scholars beginning to challenge view that the rise of democratic values belongs solely to Western secular thought. http://www.thejewishweek.com/general_topology

Skip to Navigation The Jewish Week Newsletters Print Subscriptions ... New Password MY JWEEK Write a Letter Photo Galleries Polls New Member Signup ... Live Chat Search this site: General topology Did The Hebrew Bible Give Birth To Democracy? tweetmeme_url = 'http://www.thejewishweek.com/arts/books/did_hebrew_bible_give_birth_democracy_0'; Scholars beginning to challenge view that the rise of democratic values belongs solely to Western secular thought. Eric Herschthal Staff Writer Read more: Books Entertainment Jerusalem Compactification ... Add new comment Email article Celtic-Klez tweetmeme_url = 'http://www.thejewishweek.com/arts/music/celtic_klez'; Dublin native Carl Nelkin synthesizes his dual musical heritages and releases an Irish-inflected Holocaust album. Sharon Udasin Staff Writer Standing on the bima behind a golden menorah, an emerald green leprechaun read from the megillah last Purim, a plush green top hat perched on his head and a red Irish-chasidish beard glued onto his flushed cheeks. Read more: Music Dublin Laredo New York City ... Add new comment Email article News Features Special Sections Arts ... Blogs News New York News National News International News Israel ... JInsider Opinion Editorials Gary Rosenblatt Opinion Letters ... The Last Word Features A New York Minute All She Wrote Campus Confidential Culture View ... The Nosh Pit Special Sections 36 Under 36 Arts Preview Education and Careers Healthcare ... Text - Context The Arts Arts Guide Books Dance Film ... Theater Blogs

19. 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.

20. 54: General Topology From Dave Rusin's Known Math collection. http://www.math.niu.edu/~rusin/known-math/index/54-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 54: General topology Introduction More formally, a topological space is a set X on which we have a topology a collection of subsets of X which we call the "open" subsets of X. The only requirements are that both X itself and the empty subset must be among the open sets, that all unions of open sets are open, and that the intersection of two open sets be open. This definition is arranged to meet the intent of the opening paragraph. However, stated in this generality, topological spaces can be quite bizarre; for example, in most other disciplines of mathematics, the only topologies on finite sets are the discrete topologies (all subsets are open), but the definition permits many others. Thus a general theme in topology is to test the extent to which the axioms force the kind of structure one expects to use and then, as appropriate, introduce other axioms so as to better match the intended application. For example, a single point need not be a closed set in a topology. Does this seem "inappropriate"? Then perhaps you are envisioning a special kind of topological space, say a a metric space. This alone still need not imply the space looks enough like the shapes you may have seen in a textbook; if you really prefer to understand those shapes, you need to add the axioms of a manifold, perhaps. Many such levels of generality are possible.

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