From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2103 Path: news.gmane.org!not-for-mail From: Peter McBurney Newsgroups: gmane.science.mathematics.categories Subject: Generalization of Browder's F.P. Theorem? Date: Wed, 15 Jan 2003 14:00:32 +0000 Message-ID: <3E256980.AEFD39A1@csc.liv.ac.uk> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018414 2500 80.91.229.2 (29 Apr 2009 15:20:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:20:14 +0000 (UTC) To: CATEGORIES LIST Original-X-From: rrosebru@mta.ca Wed Jan 15 15:03:04 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 15 Jan 2003 15:03:04 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18Ysn5-0002v1-00 for categories-list@mta.ca; Wed, 15 Jan 2003 15:01:31 -0400 X-Mailer: Mozilla 4.79 [en] (X11; U; Linux 2.4.18-10 i686) X-Accept-Language: en Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 28 Original-Lines: 36 Xref: news.gmane.org gmane.science.mathematics.categories:2103 Archived-At: Hello -- Does anyone know of a generalization of Browder's Fixed Point Theorem from R^n to arbitrary topological spaces, or to categories of same? ***************** Theorem (Browder, 1960): Suppose that S is a non-empty, compact, convex subset of R^n, and let f: [0,1] x S --> S be a continuous function. Then the set of fixed points { (x,s) | s = f(x,s), x \in [0,1] and s \in S } contains a connected subset A such that the intersection of A with {0} x S is non-empty and the intersection of A with {1} x S is non-empty. ***************** Many thanks, -- Peter McBurney University of Liverpool, UK