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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The semicellularity theorem


Author: Gene G. Garza
Journal: Trans. Amer. Math. Soc. 269 (1982), 663-676
MSC: Primary 57N60; Secondary 57M30
DOI: https://doi.org/10.1090/S0002-9947-1982-0637716-1
MathSciNet review: 637716
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Abstract: In this paper are proved several theorems concerning semicellularity of subsets of $ 2$-spheres in $ {E^3}$. In particular, it is shown that a cellular arc or disk on a $ 2$-sphere which has no nonpiercing points is semicellular in both complementary domains of the $ 2$-sphere. The proof is entirely geometrical and involves the idea of piercing points.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0637716-1
Article copyright: © Copyright 1982 American Mathematical Society