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
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