From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6823 Path: news.gmane.org!not-for-mail From: claudio pisani Newsgroups: gmane.science.mathematics.categories Subject: (unknown) Date: Sun, 14 Aug 2011 21:08:49 +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 1313379475 17657 80.91.229.12 (15 Aug 2011 03:37:55 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 15 Aug 2011 03:37:55 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Mon Aug 15 05:37:51 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 1Qsnzq-0002fu-Hg for gsmc-categories@m.gmane.org; Mon, 15 Aug 2011 05:37:50 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45627) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1Qsnxt-0005st-Dn; Mon, 15 Aug 2011 00:35:49 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qsnxs-0003UY-Q8 for categories-list@mlist.mta.ca; Mon, 15 Aug 2011 00:35:48 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6823 Archived-At: Dear categorists (and topologists),=0A=0Ait is known (Clementino, Hofmann, = Tholen, Richter, Niefield...) that perfect =0Amaps p:X->Y are exponentiable= in Top/Y, and that the same holds for local =0Ahomeomorphisms h:X->Y.=0A= =0AQuestion: is it true that=0A=0A1) p=3D>h is a local homeomorphism=0A=0A2= ) h=3D>p is a perfect map?=0A=0AThe conjecture is suggested by the followin= g observations:=0A=0AA) it holds both for Y =3D 1 (compact and discrete spa= ce) and for subspaces =0Ainclusion (closed and open parts)=0A=0AB) the anal= ogy between perfect maps and local homeomorphisms with discrete =0A(op)fibr= ations (via convergence or other considerations) and the fact that 1) =0Aan= d 2) above hold in Cat/Y: if p is a discrete fibration and h is a discrete = =0Aopfibration then p=3D>h is itself a discrete opfibration (and conversely= ).=0A=0ABest regards,=0A=0AClaudio [For admin and other information see: http://www.mta.ca/~cat-dist/ ]