Sheaf theoretic cohomological dimension and finitistic spaces

Author:
Satya Deo

Journal:
Proc. Amer. Math. Soc. **86** (1982), 545-550

MSC:
Primary 55N30; Secondary 54F45, 55M10

DOI:
https://doi.org/10.1090/S0002-9939-1982-0671233-3

MathSciNet review:
671233

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Abstract | References | Similar Articles | Additional Information

Abstract: For a topological -manifold , we proved earlier [**7**] that , if ; and, for a zero-dimensional manifold (discrete space) we observed that . The question was later raised as to what are those paracompact spaces, besides discrete one, for which . In this paper we prove that there is none, i.e., if is not discrete then . Another question which cropped up only recently in the cohomological theory of topological transformation groups is whether or not there exists a finitistic space which is not of finite (sheaf theoretic) integral cohomological dimension. We show that this question is related to a famous unsolved problem of cohomological dimension theory.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0671233-3

Keywords:
Sheaves,
family of supports,
sheaf theoretic cohomological dimension,
real-compactness,
finitistic spaces

Article copyright:
© Copyright 1982
American Mathematical Society