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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the shape of torus-like continua and compact connected topological groups


Author: James Keesling
Journal: Proc. Amer. Math. Soc. 40 (1973), 297-302
MSC: Primary 54C56; Secondary 22C05
MathSciNet review: 0319140
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Abstract: In this paper it is shown that if $ X$ is a torus-like continuum, then $ X$ has the shape of a compact connected abelian topological group. Let $ \Pi $ be a collection of compact connected Lie groups. In light of the above result it is natural to ask if a $ \Pi $-like continuum has the shape of a compact connected topological group. An example is given to show that this is not the case.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0319140-4
PII: S 0002-9939(1973)0319140-4
Keywords: Torus-like continuum, shape, compact connected abelian topological group, compact connected topological group, Čech cohomology, property $ {\text{L}}$, movability
Article copyright: © Copyright 1973 American Mathematical Society