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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Additional Information
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