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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Some examples in shape theory using the theory of compact connected abelian topological groups


Author: James Keesling
Journal: Trans. Amer. Math. Soc. 219 (1976), 169-188
MSC: Primary 55D99; Secondary 22C05
MathSciNet review: 0436134
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Abstract: In previous papers the author has studied the shape of compact connected abelian topological groups. This study has led to a number of theorems and examples in shape theory. In this paper a theorem is proved concerning the Čech homology of compact connected abelian topological groups. This theorem together with the author's previous results are then used to study the movability of general compact Hausdorff spaces. In the theory of shape for compact metric spaces, a number of significant theorems have been proved for movable compact metric spaces. Among these are a theorem of Hurewicz type due to K. Kuperberg, a Whitehead type theorem due to Moszyńska, and a theorem concerning the exactness of the Čech homology sequence for movable compact metric pairs due to Overton. In this paper examples are constructed which show that these theorems do not generalize to arbitrary movable compact Hausdorff spaces without additional assumptions.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0436134-6
PII: S 0002-9947(1976)0436134-6
Keywords: Shape theory, movable space, Čech homology, Hurewicz type theorem, Whitehead type theorem, exactness of Čech homology, compact connected abelian topological group
Article copyright: © Copyright 1976 American Mathematical Society