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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: David A. Edwards and Ross Geoghegan
Journal: Trans. Amer. Math. Soc. 214 (1975), 261-277
MSC: Primary 55D99; Secondary 54C56
MathSciNet review: 0413095
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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).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0413095-6
PII: S 0002-9947(1975)0413095-6
Article copyright: © Copyright 1975 American Mathematical Society