From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2551 Path: news.gmane.org!not-for-mail From: Gabor Lukacs Newsgroups: gmane.science.mathematics.categories Subject: Compact subsets of k-spaces (without separation axioms) Date: Sun, 15 Feb 2004 08:47:57 -0500 (EST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018741 4693 80.91.229.2 (29 Apr 2009 15:25:41 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:25:41 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Sun Feb 15 17:19:00 2004 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 15 Feb 2004 17:19:00 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1AsTeX-0002T0-00 for categories-list@mta.ca; Sun, 15 Feb 2004 17:18:13 -0400 X-X-Sender: Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 12 Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:2551 Archived-At: Dear Topologists, Categorists and Categorical Topologists, It is well-known that for a *Hausdorff* topological space X, its k-ification kX and X have the same compact subspaces. It is also well-known that when we assume no separation axioms, X and kX have the same k-continuous maps (i.e. maps f:X -->Y such that ft is continuous for every "test-function" t: K --> X, where K is a compact Hausdorff space). I was wondering if anyone knows whether the first statement is true *without separation axioms*, i.e., whether for every topological space X, its k-ification kX and X have the same compact subspaces. I would very much appreciate any suggestion, reference or counterexample. Gabor Lukacs