Subject: RE: 2 questions Date: Wed, 8 May 2002 13:08:08 -0400 From: "David Hurtubise" To: "Don Davis" In the paper, "On Axiomatic Homology Theory" by J. Milnor, Pacific J. Math. 12, 1962 p. 338 Milnor states: Let K_1 \subset K_2 \subset \cdots $ be CW-complexes with union $K$... Let $L$ denote the CW-complex $$ L = K_1 \times [0,1] \cup K_2 \times [1,2] \cup K_3 \times [2,3] \cup \cdots ; $$ contained in $K \times [0,\infty)$. The projection map $L \rightarrow K$ induces isomorphisms of homotopy groups in all dimensions, and therefore is a homotopy equivalence. (See Whitehead [6, Theorem 1]." ------------------------------------------ David E. Hurtubise Mathematics Degree Coordinator Department of Mathematics and Statistics Penn State Altoona Altoona, PA 16601-3760 http://www.personal.psu.edu/dxh40 -----Original Message----- From: Don Davis [mailto:dmd1@lehigh.edu] Sent: Wednesday, May 08, 2002 11:49 AM To: dmd1@lehigh.edu (Don Davis) Subject: 2 questions 2 postings---both are questions........DMD ___________________________________________ Subject: question for the toplist Date: Sun, 5 May 2002 09:33:53 +0100 (GMT Daylight Time) From: Andrey Lazarev Here's another question on homotopy limits. Is it true that the homotopy limit of a diagram of CW-complexes has homotopy type of a CW-complex? Thanks, Andrey --------------------------------------- Andrey Lazarev A.Lazarev@bristol.ac.uk Phone +44 117 928 7997 School of Mathematics University of Bristol Bristol BS8 1TW UK ---------------------------------------