The semicellularity theorem

Garza, Gene G.

doi:10.1090/S0002-9947-1982-0637716-1

The semicellularity theorem
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Trans. Amer. Math. Soc. 269 (1982), 663-676 Request permission

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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