From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5041 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: separable locale Date: Sun, 5 Jul 2009 21:54:50 +0100 (BST) Message-ID: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1247189531 30217 80.91.229.12 (10 Jul 2009 01:32:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Fri, 10 Jul 2009 01:32:11 +0000 (UTC) To: Thomas Streicher , categories@mta.ca Original-X-From: categories@mta.ca Fri Jul 10 03:32:04 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 1MP4y2-0008LJ-7N for gsmc-categories@m.gmane.org; Fri, 10 Jul 2009 03:32:02 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MP4Jz-0003I3-Tj for categories-list@mta.ca; Thu, 09 Jul 2009 21:50:39 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5041 Archived-At: 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/ ]