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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Embeddings of compacta with shape dimension in the trivial range


Author: Gerard A. Venema
Journal: Proc. Amer. Math. Soc. 55 (1976), 443-448
DOI: https://doi.org/10.1090/S0002-9939-1976-0397738-8
MathSciNet review: 0397738
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Abstract: In this paper a loop condition is defined which generalizes the cellularity criterion and applies to compacta with nontrivial shape. It is shown that if $ X,Y \subset {E^n},n \geqslant 5$, are compacta which satisfy this loop condition and whose shape classes include a space having dimension in the trivial range with respect to $ n$, then $ \operatorname{Sh} (X) = \operatorname{Sh} (Y)$ is equivalent to $ {E^n} - X \approx {E^n} - Y$. An application is given to compacta with the shape of a compact connected abelian topological group.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0397738-8
Keywords: Shape, loop conditions, weak flatness
Article copyright: © Copyright 1976 American Mathematical Society