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 ---------------------------------------