From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4642 Path: news.gmane.org!not-for-mail From: wlawvere@buffalo.edu Newsgroups: gmane.science.mathematics.categories Subject: Re: Group and abelian group objects in the category of Kelley spaces Date: Mon, 29 Sep 2008 11:19:12 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241020076 14171 80.91.229.2 (29 Apr 2009 15:47:56 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:47:56 +0000 (UTC) To: , "Bill Rowan" , "Jeff Egger" Original-X-From: rrosebru@mta.ca Mon Sep 29 15:37:29 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 29 Sep 2008 15:37:29 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KkNVq-00022K-26 for categories-list@mta.ca; Mon, 29 Sep 2008 15:30:26 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 138 Original-Lines: 45 Xref: news.gmane.org gmane.science.mathematics.categories:4642 Archived-At: The term "Kelley space" is a misnomer (due to Gabriel & Zisman ?), resulting from a misinterpretation of the prefix in "k-space". JLK's excellent 1955 textbook, from which=20 many of us learned mathematics, was not doing subtle self-promotion when he used that term in=20 his clear exposition. In fact, "k" stands for kompakt, and the term was used by Hurewicz in his 1949 lectures at Princeton where he introduced these spaces. I have that from telephone discussions with the late David Gale, who had mentioned Hurewicz's k-spaces in his=20 1950 PAMS paper (as noticed by Horst Herrlich). The same implicit idea is used in RH Fox's 1945 paper (except based on countable=20 compact spaces instead of all), which was directly incited by a letter from Hurewicz. Bill On Mon 09/29/08 6:36 AM , Jeff Egger jeffegger@yahoo.ca sent: > > if we have an (abelian, say) > > topological group, there is a natural uniform > topology on> the group such > > that the operations are uniformly continuous.=20 > Does the> same hold for > > abelian group objects in the category of Kelley > spaces? > As others have already noted, the answer is no. One possible > solution (assuming you regard this as a defect) is to apply > the idea implicit in the definition of Kelley space, not to > the category of all topological spaces, but to that of all > Tychonov (=3Duniformisable) spaces. What results is a cartesian > closed category (that of "k_R-Tychonov spaces") with somewhat > different properties; a group in this category is tautologously > uniformisable and, if I recall correctly, is also true that the > operations are uniformly continuous. Gabor Lukacs has studied > these things and spoken about them at several conferences. >=20 > Cheers, > Jeff.