Embeddings of compacta with shape dimension in the trivial range

Venema, Gerard A.

doi:10.1090/S0002-9939-1976-0397738-8

Embeddings of compacta with shape dimension in the trivial range
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by Gerard A. Venema PDF

Proc. Amer. Math. Soc. 55 (1976), 443-448 Request permission

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

Journal: Proc. Amer. Math. Soc. 55 (1976), 443-448
DOI: https://doi.org/10.1090/S0002-9939-1976-0397738-8
MathSciNet review: 0397738