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         Topological Groups:     more books (100)
  1. Topological Groups 1ST Edition by Leon Pontrjagin, 1939
  2. Topological Groups: Characters, Dualities, and Minimal Group Topoligies (Pure and Applied Mathematics) (Vol 130) by Dikran N. Dikranjan, Ivan R. Prodanov, et all 1989-09-26
  3. Cohomology Theory of Topological Transformation Groups (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge) by W.Y. Hsiang, 1975-08-26
  4. Stratified Lie Groups and Potential Theory for Their Sub-Laplacians (Springer Monographs in Mathematics) by Andrea Bonfiglioli, Ermanno Lanconelli, et all 2010-11-02
  5. Compact Lie Groups (Graduate Texts in Mathematics) by Mark R. Sepanski, 2010-11-02
  6. Lie Groups and Lie Algebras III: Structure of Lie Groups and Lie Algebras (Encyclopaedia of Mathematical Sciences)
  7. Stochastic Processes in Non-archimedean Banach Spaces, Manifolds and Topological Groups
  8. Classical Topology and Combinatorial Group Theory by John Stillwell, 1993-03-25
  9. Exercises in Abelian Group Theory (Texts in the Mathematical Sciences) by D. Valcan, C. Pelea, et all 2010-11-02
  10. Applications of the Theory of Groups in Mechanics and Physics (Fundamental Theories of Physics) by Petre P. Teodorescu, Nicolae-A.P. Nicorovici, 2010-11-02
  11. Generalized Heisenberg Groups and Damek-Ricci Harmonic Spaces (Lecture Notes in Mathematics) by J├╝rgen Berndt, Franco Tricerri, et all 1995-04-13
  12. Representation Theory of Algebraic Groups and Quantum Groups (Progress in Mathematics)
  13. Elements of Topological Dynamics (Mathematics and Its Applications) by J. de Vries, 2010-11-02
  14. Profinite Groups (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge A Series of Modern Surveys in Mathematics) by Luis Ribes, Pavel Zalesskii, 2010-11-02

41. Topological Groups
topological groups Topology Geometry discussion Vote for Physics Forums in the physics.org Best Q A site category! (you have to register) Vote here
http://www.physicsforums.com/showthread.php?t=302073

42. [math/0004119] On Subgroups Of Minimal Topological Groups
by VV Uspenskij 2000 - Cited by 23 - Related articles
http://arxiv.org/abs/math/0004119
arXiv.org math
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Title: On subgroups of minimal topological groups
Authors: V.V. Uspenskij (Submitted on 19 Apr 2000 ( ), last revised 15 Mar 2007 (this version, v2)) Abstract: A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. The Roelcke uniformity (or lower uniformity) on a topological group is the greatest lower bound of the left and right uniformities. A group is Roelcke-precompact if it is precompact with respect to the Roelcke uniformity. Many naturally arising non-Abelian topological groups are Roelcke-precompact and hence have a natural compactification. We use such compactifications to prove that some groups of isometries are minimal. In particular, if U_1 is the Urysohn universal metric space of diameter 1, the group Iso(U_1) of all self-isometries of U_1 is Roelcke-precompact, topologically simple and minimal. We also show that every topological group is a subgroup of a minimal topologically simple Roelcke-precompact group of the form Iso(M), where M is an appropriate non-separable version of the Urysohn space. Comments: To appear in Topology and its Applications. 39 pages

43. Topological Groups
Selected openaccess documents for Topological Groups, with related authors
http://unjobs.org/tags/topological-groups

44. Topological Groups
iv, 50 p. Title Topological Groups Author Rapley, William Henry Abstract The purpose of this paper is to introduce the reader to the field of topological groups.
http://scholar.simmons.edu/handle/10090/16211

45. Topological Group
The real numbers with the standard topology form a topological group. More generally, an ordered group with its order topology is a topological group.
http://myyn.org/m/article/topological-group2/

46. Categories: Re: Abelian Topological Groups
One thing is clear your ideal abelian category is not abelian. Furthermore, you don't get to choose your sub and quotient objects; they are imposed by the category.
http://north.ecc.edu/alsani/ct01(5-8)/msg00001.html
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categories: Re: Abelian Topological Groups

47. Topological Group
Every group can be made into a topological group by imposing the discrete topology on it. However, the more interesting situation is where the group has
http://www.fact-index.com/t/to/topological_group.html
Main Page See live article Alphabetical index
Topological group
In mathematics , a topological group G is a group that is also a topological space such that the group multiplication
G G G
and taking inverses
G G
are continuous maps. Here, G G is viewed as a topological space by using the product topology . (See group object Though we do not do so here, it is common to also require that the topology on G be Hausdorff . The reasons, and some equivalent conditions, are discussed below. Almost all objects investigated in analysis are topological groups (usually with some additional structure). Every group can be made into a topological group by imposing the discrete topology on it. However, the more interesting situation is where the group has some other topology, not arising so directly from the group operation. Table of contents 1 Examples
2 Properties

3 Relationship to other areas of mathematics
Examples
The real numbers R , together with addition as operation and its ordinary topology, form a topological group. More generally, Euclidean n -space R n with addition and standard topology is a topological group. More generally still, all topological vector spaces, such as Banach spaces or Hilbert spaces, are topological groups.

48. Fuzzy Topological Groups
File Format PDF/Adobe Acrobat Quick View
http://personalpages.manchester.ac.uk/staff/david.foster/Research/My_PDFs/Foster

49. Categories: Abelian Topological Groups
I am attempting to construct the ideal abelian category within which live complete, hausdorff abelian topological groups. The idea is that the quotients of such a group, in the
http://north.ecc.edu/alsani/ct01(5-8)/msg00000.html
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categories: Abelian Topological Groups

50. About "Topological Groups, Lie Groups"
A short article designed to provide an introduction to Lie groups, an important special branch of group theory.......Author Dave Rusin; The Mathematical Atlas
http://mathforum.org/library/view/7591.html
Topological Groups, Lie Groups
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Visit this site: http://www.math.niu.edu/~rusin/known-math/index/22-XX.html Author: Dave Rusin; The Mathematical Atlas Description: A short article designed to provide an introduction to Lie groups, an important special branch of group theory. They have algebraic structure and yet are also subsets of space, and so have a geometry; moreover, portions of them look just like Euclidean space, making it possible to do analysis on them (e.g. solve differential equations). Thus Lie groups and other topological groups lie at the convergence of the different areas of pure mathematics. (They are quite useful in application of mathematics to the sciences as well.) History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. Levels: College Languages: English Resource Types: Articles Math Topics: Topological Groups/Lie Groups
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51. International Workshop On Topological Groups. Universidad De Navarra.
We are pleased to announce a Workshop on topological groups. The meeting will take place August 31stSeptember 2nd, 2005 at the Universidad de Navarra,
http://www.unav.es/topology/
response.write ("") International Workshop on Topological Groups Pamplona, August 31st - September 2nd Main Page Accomodation Registration Location ... Department of Physics and Mathematics International Workshop on Topological Groups.
Pamplona, August 31st - September 2nd
We are pleased to announce a Workshop on topological groups.
The meeting will take place August 31st-September 2nd, 2005 at the Universidad de Navarra, Pamplona (Spain).
The registration fee is 100 Eur. before July 31st and 120 Eur. for late registrations.
First Day Notices
Conference check in will be on Wednesday August 31st, in the Entrance Hall of the Sciences Building (see map for the location) between 9 and 9:30.
The opening ceremony will take place at 9:30 in the "Salon the actos", room located next to the check in table.
The lectures (see updated schedule ) will all take place in Room 3A02 on the third floor of the same building.
Panels for posters will be located next to room 3A02.
Scientific Program This workshop is directed to Graduate students and all researchers interested on topological groups.

52. Fundamental Group As Topological Group - MathOverflow
2 Daniel K. Biss, The topological fundamental group and generalized covering spaces , Topology and its Applications, Vol. 124
http://mathoverflow.net/questions/26680/fundamental-group-as-topological-group
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Fundamental group as topological group
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Background
[1] Daniel K. Biss, A Generalized Approach to the Fundamental Group, The American Mathematical Monthly, Vol. 107 You can find this online . This is somehow an introduction to [2] Daniel K. Biss, The topological fundamental group and generalized covering spaces , Topology and its Applications, Vol. 124
Question
An example that products of quotient maps don't have to be quotient maps can be found here . Remark however that this is true in the category of compactly generated spaces. at.algebraic-topology gn.general-topology topological-groups flag edited Jun 1 at 13:05
asked Jun 1 at 8:01 Martin Brandenburg
Andrew Stacey
Jun 1 at 11:09 Tyler Lawson Jun 1 at 12:52 Jeremy Brazas Jun 1 at 14:40
4 Answers
oldest newest votes
Update : A bit of a digital paper chase led me, via David Robert's thesis (note that in the latest version, it is Chapter 5, section 2 that is most relevant), to this paper on the arXiv. The last sentence of the abstract is:

53. CRC Press Online - Book: Topological Groups
Algebraic and Differential Topology R. V. Gamkrelidze Publication Date March 06, 1987 Price $129.95
http://www.crcpress.com/product/isbn/9782881241338
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54. JSTOR: An Error Occurred Setting Your User Cookie
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55. Topological Groups
In any topological group, the connected component of the identity is a closed normal subgroup and the quotient is totally disconnected. the singletons of which as
http://sci.tech-archive.net/Archive/sci.math/2005-06/msg01906.html
Topological groups
  • From Date : Sun, 12 Jun 2005 23:34:24 -0700

Newsgroups: sci.math
Subject: Re: Topological groups
Thank you for the excellent summary.
Let G be a topological group and H = C(e).
Then yes, H is closed normal subgroup.
If K connected subgroup, then as e in K, K subset H = C(e)
I dispute the converse.
If G = R, then C(0) = R and Z subset R is not connected.
In particular C(a) = aC(e) = aH
bijection between the components of G and the elements of G/H, the singletons of which as you claim are the components of G/H. That G is connected when G/H is follows from Am I right, that the following are theorems the same for closed maps, and that with the same premises plus continuous surjection But why not Why of course, are not components saturated for f? ie G/H is totally disconnected? outline of proof some u in U, v in V with y = f(u) = f(v) u,v in f^-1(y) subset f^-1(K); U,V disconnect f^-1(y), no! open f(U), f(V) disconnect K, no!

56. A KUROSH SUBGROUP THEOREM FOR TOPOLOGICAL GROUPS
Your browser may not have a PDF reader available. Google recommends visiting our text version of this document.
http://plms.oxfordjournals.org/cgi/reprint/s3-42/3/461.pdf

57. Wiley::Topological Groups: An Introduction
A userfriendly introduction to metric and topological groups. Topological Groups An Introduction provides a self-contained presentation with an emphasis on important families of
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470624515.html?cid=RSS_WILEY

58. Algebraic Cohomology Of Topological Groups Author(s) David Wigner
File Format PDF/Adobe Acrobat Quick View
http://egg.epfl.ch/~nmonod/bonn/Wigner_1973.pdf

59. The Math Forum - Math Library - Topo./Lie Groups
Topological Groups, Lie Groups Dave Rusin; The Mathematical Atlas A short article designed to provide an introduction to Lie groups, an important special branch of group theory.
http://mathforum.org/library/topics/group_topol/
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  • Topological Groups, Lie Groups - Dave Rusin; The Mathematical Atlas
    A short article designed to provide an introduction to Lie groups, an important special branch of group theory. They have algebraic structure and yet are also subsets of space, and so have a geometry; moreover, portions of them look just like Euclidean space, making it possible to do analysis on them (e.g. solve differential equations). Thus Lie groups and other topological groups lie at the convergence of the different areas of pure mathematics. (They are quite useful in application of mathematics to the sciences as well.) History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>
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  • CT Category Theory (Front for the Mathematics ArXiv) - Univ. of California, Davis
  • 60. Wiley::Topological Groups: An Introduction
    Topological Groups An Introduction provides a selfcontained presentation with an emphasis on important families of topological groups.
    http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0470624515.html?cid=RSS_WILEY2

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