From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5046 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: Re: separable locale Date: Fri, 10 Jul 2009 00:32:02 -0300 Message-ID: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.gmane.org Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1247228044 23992 80.91.229.12 (10 Jul 2009 12:14:04 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 10 Jul 2009 12:14:04 +0000 (UTC) To: "Prof. Peter Johnstone" , categories@mta.ca Original-X-From: categories@mta.ca Fri Jul 10 14:13:58 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MPEzF-0004Pe-2N for gsmc-categories@m.gmane.org; Fri, 10 Jul 2009 14:13:57 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MPEER-0001IG-8J for categories-list@mta.ca; Fri, 10 Jul 2009 08:25:35 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5046 Archived-At: "separable" is used also to mean T_2 Prof. Peter Johnstone wrote: > Dear Thomas, > > I'm pretty sure that what Michael meant by "separable" was what > most topologists would call "second countable" -- i.e., countably > generated as a frame. (There are some topology textbooks in which > this condition is called "completely separable".) > > Peter Johnstone > --------------------------------- > On Tue, 30 Jun 2009, Thomas Streicher wrote: > >> Recently rereading Fourman's "Continuous Truth" I came across the term >> "separable locale" but could nowhere find an explanation. Does it mean a >> cHa A for which there exists a countable subset B such that ever a in >> A is >> the supremum of those b in B with b leq a. This would be the point free >> account of "second countable", i.e. having a countable basis. >> Of course, second countable T_) spaces are separable, i.e. have a >> countable >> dense set. >> Is this reading the "usual" one? >> >> Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]