Subject: clarification
Date: Thu, 9 May 2002 09:25:38 +0100 (GMT Daylight Time)
From: Andrey Lazarev
To: Don Davis
Dear Don,
could you post the following clarification of my original question?
--------------------------------------------------------------------
Perhaps I should clarify my question. Let D:I-->Top
be a diagram of topological spaces (say, pointed, compactly
generated, weakly Hausdorff). Here the indexing category I is not
necessarily a directed set. Then we could form its homotopy (inverse)
limit holim(D). I insist that the diagram D consist of CW-complexes.
Question: is it true that holim(D) has homotopy type of a CW-complex?
Note that it is important that we take the inverse limit. In the case
of the homotopy direct limit the answer is positive and is a more or
less a model category theory result. (hocolim of the object-wise
cofibrant diagram is cofibrant.)
---------------------------------------
Andrey Lazarev
A.Lazarev@bristol.ac.uk
Phone +44 117 928 7997
School of Mathematics
University of Bristol
Bristol BS8 1TW UK
---------------------------------------