Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



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
MathSciNet review: 0270353
Full-text PDF Free Access

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.78, 57.00

Retrieve articles in all journals with MSC: 54.78, 57.00

Additional Information

Keywords: Cellularity criterion, $ 1$-complex, $ 1$-LC, LPU
Article copyright: © Copyright 1970 American Mathematical Society