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


A loop condition for embedded compacts

Authors: D. Coram, R. J. Daverman and P. F. Duvall
Journal: Proc. Amer. Math. Soc. 53 (1975), 205-212
MSC: Primary 57A60; Secondary 57A40
MathSciNet review: 0377902
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Abstract: In this paper we consider a version $ ({\text{SLC}})$ of the cellularity criterion which applies to embeddings of arbitrary compacta. It is shown that if the continuum $ X \subset {E^n},\;\dim X \leqslant n - 3$, has the shape of a finite $ k$-complex $ K,\;2k + 1 \leqslant n$, and satisfies the $ {\text{SLC}}$, then $ X$ has arbitrarily small neighborhoods which are regular neighborhoods of a copy of $ K$.

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PII: S 0002-9939(1975)0377902-3
Keywords: Cellularity criterion, regular neighborhood, $ UV$ properties
Article copyright: © Copyright 1975 American Mathematical Society