From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6824 Path: news.gmane.org!not-for-mail From: claudio pisani Newsgroups: gmane.science.mathematics.categories Subject: exponentials of perfect maps and local homeomorphisms Date: Mon, 15 Aug 2011 05:54:27 +0100 (BST) Message-ID: Reply-To: claudio pisani NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1313387402 20156 80.91.229.12 (15 Aug 2011 05:50:02 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 15 Aug 2011 05:50:02 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Mon Aug 15 07:49:54 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Qsq3e-0007ry-6s for gsmc-categories@m.gmane.org; Mon, 15 Aug 2011 07:49:54 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46792) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1Qsq1N-0006US-4e; Mon, 15 Aug 2011 02:47:33 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qsq1M-0003kV-FB for categories-list@mlist.mta.ca; Mon, 15 Aug 2011 02:47:32 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6824 Archived-At: Dear categorists (and topologists), It is known (Clementino, Hofmann, Tholen, Richter, Niefield...) that perfect maps p:X->Y are exponentiable in Top/Y, and that the same holds for local homeomorphisms h:X->Y. Question: is it true that 1) p=>h is a local homeomorphism) h=>p is a perfect map? The conjecture is suggested by the following observations: A) it holds both for Y = 1 (compact and discrete space) and for subspaces = inclusion (closed and open parts) B) the analogy between perfect maps and local homeomorphisms with discrete (op)fibrations (via convergence or other considerations) and the fact that 1) and 2) above hold in Cat/Y: if p is a discrete fibration and h is a discrete opfibration then p=>h is itself a discrete opfibration (and conversely). Best regards, Claudio [For admin and other information see: http://www.mta.ca/~cat-dist/ ]