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, dim_G 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, dim_G 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, dim_G X <= 2 and dim_G X <= 1 if G is finite.

These theorems improve on results of Dranishnikov, Dydak, Miyata, Repovs and Walsh.

Date received: January 26, 2000