The Čech cohomology of movable and -movable spaces

Author:
James Keesling

Journal:
Trans. Amer. Math. Soc. **219** (1976), 149-167

MSC:
Primary 55B05; Secondary 54C56

MathSciNet review:
0407829

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Abstract: In this paper the Čech cohomology of movable and *n*-movable spaces is studied. Let *X* be a space and let denote the *k*-dimensional Čech cohomology of *X* with integer coefficients based on the numerable covers of *X*. Then if *X* is movable, there is a subgroup *E* of which is the union of all the algebraically compact subgroups of . Furthermore, is an -free abelian group. If *X* is an *n*-movable space, then it is shown that this structure holds for for and may be false for . If *X* is an paracompactum, then *X* is known to be *n*-movable. However, in this case and in the case that *X* is an compactum a stronger structure theorem is proved for for than that stated above. Using these results examples are given of *n*-movable continua that are not shape equivalent to any paracompactum.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1976-0407829-5

Keywords:
Shape theory,
movable space,
*n*-movable space,
paracompactum,
Čech cohomology

Article copyright:
© Copyright 1976
American Mathematical Society