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

Edwards, David A.; Geoghegan, Ross

doi:10.1090/S0002-9947-1975-0413095-6

The stability problem in shape, and a Whitehead theorem in pro-homotopy
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by David A. Edwards and Ross Geoghegan

Trans. Amer. Math. Soc. 214 (1975), 261-277

DOI: https://doi.org/10.1090/S0002-9947-1975-0413095-6

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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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