The stability problem in shape, and a Whitehead theorem in pro-homotopy-Reference-Cited by-同舟云学术

The stability problem in shape, and a Whitehead theorem in pro-homotopy

Published:1975 Issue:0 Volume:214 Page:261-277
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Edwards David A.,Geoghegan Ross

Abstract

Theorem 3.1 is a Whitehead theorem in pro-homotopy for finite-dimensional pro-complexes. This is used to obtain necessary and sufficient algebraic conditions for a finite-dimensional tower of complexes to be pro-homotopy equivalent to a complex (§4) and for a finite-dimensional compact metric space to be pointed shape equivalent to an absolute neighborhood retract (§5).

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1975-214-00/S0002-9947-1975-0413095-6/S0002-9947-1975-0413095-6.pdf

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1. Shape Theory;Journal of Mathematical Sciences;2021-11-16

2. History of Shape Theory and its Application to General Topology;Handbook of the History of General Topology;2001

3. Absolute Neighborhood Retracts and Shape Theory;History of Topology;1999

4. Stability in pro-homotopy theory;Proceedings of the Edinburgh Mathematical Society;1990-10

5. Theory of shapes. I;Journal of Soviet Mathematics;1983