Subject: fixed points
Date: Wed, 14 Nov 2001 12:30:39 -0600
From: Philip Reny <p-reny@uchicago.edu>
To: dmd1@lehigh.edu

Daer Professor Davis: I'm an economics professor at The University of
Chicago. Professor Peter May suggested that I contact you regarding the
following question relevant to my current research.

Suppose that X is a nonempty, compact, contractible, metrizable subset of a
locally convex linear topological space.
(i) Is X an absolute neighborhood retract? (If so, is there a reference for
such a result?)
(ii) If the answer to (i) is "not necessarily," then suppose in addition
that F is a point to set mapping on X with a closed graph such that F(x) is
nonempty and contractible for every x in X. Must F possess a fixed point?
(Obviously an affirmative answer to (i) implies an affirmative answer to
(ii).)

I would be grateful if you could post this question onto your algebraic
topology discussion group site. Best wishes.
Phil Reny

************************
Philip Reny
Department of Economics
University of Chicago
1126 East 59th Street
Chicago, IL 60637

http://www.src.uchicago.edu/users/preny/

(O) 773-702-8192
(F) 773-702-8490