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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0270353-7
Keywords: Cellularity criterion, $ 1$-complex, $ 1$-LC, LPU
Article copyright: © Copyright 1970 American Mathematical Society

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