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Some examples in Cohomological Dimension Theorey
by
Michael Levin
Texas Tech University
The extensional dimension of X does not exceed K, written e-dimX <= K, if every map of a closed subset of X into K extends over X. We present:
Theorem 1. There is a locally compact separable metric space X such that for every abelian group G and every non-contractible CW-complex P, dimG X <= 2 and e-dim(the Stone-Cech compactification of X) > P.
Theorem 2. There is a separable metric space X such that for every abelian group G and every Hausdorff compactification X' of X, dimG X <= 2 and e-dimX' > P for every CW-complex P which is not 2-connected.
Theorem 3. There is a compactum X such that for every cyclic finite CW-complex P and every abelian group G, e-dimX > P, dimG X <= 2 and dimG X <= 1 if G is finite.
These theorems improve on results of Dranishnikov, Dydak, Miyata, Repovs and Walsh.
Date received: January 26, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cady-13.