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 Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PDF PostScript Other formats Current browse context: math new recent NASA ADS Bookmark what is this? Mathematics > General Topology 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

Date Prev Date Next Thread Prev Thread Next ... Thread Index categories: Re: Abelian Topological Groups To categories@mta.ca Subject : categories: Re: Abelian Topological Groups From barr@barrs.org Date : Wed, 2 May 2001 06:11:51 -0400 (EDT) In-Reply-To 200105010437.f414bIi14109@transbay.net Sender cat-dist@mta.ca References categories: Abelian Topological Groups From: Prev by Date: categories: Abelian Topological Groups Next by Date: categories: diaxydoc.tex Prev by thread: categories: Abelian Topological Groups Next by thread: categories: diaxydoc.tex Index(es): Date Thread

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

[Date Prev][ Date Next ][Thread Prev][ Thread Next Date Index Thread Index categories: Abelian Topological Groups To categories@mta.ca Subject : categories: Abelian Topological Groups From rowan@transbay.net Date : Mon, 30 Apr 2001 21:37:18 -0700 (PDT) Sender cat-dist@mta.ca Follow-Ups categories: Re: Abelian Topological Groups From: Next by Date: categories: Re: Abelian Topological Groups Next by thread: categories: Re: Abelian Topological Groups Index(es): Date Thread

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 Library Home Full Table of Contents Suggest a Link Library Help 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 Home The Math Library Quick Reference ... Help http://mathforum.org/ The Math Forum is a research and educational enterprise of the Goodwin College of Professional Studies

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

login faq how to ask meta ... Fundamental group as topological group Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points 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

window.RICH_FACES_EXTENDED_SKINNING_ON=true; Tell a friend about this title (Sending...) Topological Groups R. V. Gamkrelidze Price: Publication Date: March 06, 1987 * Required field Friend's Email Address* Personal Message Your Name* Your Email Address* Send me a copy of this email Security Math Problem* If you are unable to see the image, please contact customer support Email addresses entered in this form are used only for purpose of telling your friend about this title. Tell a friend about this title Your message has been sent. Region: AFGHANISTAN ALBANIA ALGERIA AMERICAN SAMOA ANDORRA ANGOLA ANGUILLA ANTARCTICA ANTIGUA AND BARBUDA ARGENTINA ARMENIA ARUBA AUSTRALIA AUSTRIA AZERBAIJAN BAHAMAS BAHRAIN BANGLADESH BARBADOS BELARUS BELGIUM BELIZE BENIN BERMUDA BHUTAN BOLIVIA BOSNIA AND HERZEGOVINA BOTSWANA BOUVET ISLAND BRAZIL BRITISH INDIAN OCEAN TERRITORY BRUNEI DARUSSALAM BULGARIA BURKINA FASO BURUNDI CAMBODIA CAMEROON CANADA CAPE VERDE CAYMAN ISLANDS CENTRAL AFRICAN REPUBLIC CHAD CHILE CHINA CHRISTMAS ISLAND COCOS (KEELING) ISLANDS COLOMBIA COMOROS CONGO CONGO, THE DEMOCRATIC REPUBLIC OF THE

54. JSTOR: An Error Occurred Setting Your User Cookie Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.jstor.org/stable/2305290

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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! Follow-Ups Re: Topological groups From: M References Topological groups From: M Re: Topological groups From: Jose Carlos Santos Re: Topological groups From: Termite of Tempation Re: Topological groups From: M Re: Topological groups From: barr Prev by Date: Re: uncountable n-tuplets?

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/

Browse and Search the Library Home Math Topics Topology : Topo./Lie Groups Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category 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>> All Sites - 9 items found, showing 1 to 9 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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