Cell-like mappings and nonmetrizable compacta of finite cohomological dimension

Mardešić, Sibe; Rubin, Leonard R.

doi:10.1090/S0002-9947-1989-0962284-0

Cell-like mappings and nonmetrizable compacta of finite cohomological dimension
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by Sibe Mardešić and Leonard R. Rubin PDF

Trans. Amer. Math. Soc. 313 (1989), 53-79 Request permission

Abstract:

Compact Hausdorff spaces $X$ of cohomological dimension ${\dim _Z}X \leq n$ are characterized as cell-like images of compact Hausdorff spaces $Z$ with covering dimension $Z \leq n$. The proof essentially uses the newly developed techniques of approximate inverse systems.

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A theorem and a question related to cohomological dimension and cell-like maps

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