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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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Keywords: Cellularity criterion, regular neighborhood, <IMG WIDTH="38" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$UV$"> properties
Article copyright: © Copyright 1975 American Mathematical Society