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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Determining the cellularity of a $i$-complex by properties of its arcs.


Author: R. B. Sher
Journal: Proc. Amer. Math. Soc. 26 (1970), 491-498
MSC: Primary 54.78; Secondary 57.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0270353-7
MathSciNet review: 0270353
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that a $1$-complex $K$ topologically embedded in the interior of a topological $n$-manifold $M,n \geq 3$, satisfies the cellularity criterion if for each arc $A$ in $K,M - A$ is $1$-LC at an endpoint of $A$. This condition is satisfied if each arc in $K$ is LPU at an endpoint. An example is given to show that it is not sufficient to suppose that each arc in $K$ satisfies the cellularity criterion.


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Keywords: Cellularity criterion, <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$1$">-complex, <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$1$">-LC, LPU
Article copyright: © Copyright 1970 American Mathematical Society