An algebraic property of the Čech cohomology groups which prevents local connectivity and movability

Author:
James Keesling

Journal:
Trans. Amer. Math. Soc. **190** (1974), 151-162

MSC:
Primary 55B05

MathSciNet review:
0367973

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *C* denote the category of compact Hausdorff spaces and be the homotopy functor. Let be the functor of shape in the sense of Holsztyński for the projection functor *H*. Let *X* be a continuum and denote *n*-dimensional Čech cohomology with integer coefficients. Let be the character group of considering as a discrete group. In this paper it is shown that there is a shape morphism such that is an isomorphism. It follows from the results of a previous paper by the author that there is a continuous mapping such that and thus that is an isomorphism. This result is applied to show that if *X* is locally connected, then has property L. Examples are given to show that *X* may be locally connected and not have property L for . The result is also applied to compact connected topological groups.

In the last section of the paper it is shown that if *X* is compact and movable, then for every integer *n*, has property L. This result allows us to construct peano continua which are nonmovable. An example is given to show that itself may not have property L even if *X* is a finite-dimensional movable continuum.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0367973-6

Keywords:
Shape functor,
Čech cohomology,
compact space,
compact connected topological group,
local connectivity,
movability,
property L,
continuous homomorphism

Article copyright:
© Copyright 1974
American Mathematical Society