A generalization of Tietze’s theorem on convex sets in 𝑅³

Stavrakas, Nick M.

doi:10.1090/S0002-9939-1973-0341280-4

A generalization of Tietze’s theorem on convex sets in $R^{3}$
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Proc. Amer. Math. Soc. 40 (1973), 565-567 Request permission

Abstract:

Let $S \subset {R^3}$ and let $C(S)$ denote the points of local convexity of $S$. One interesting result which is proven is Theorem. Let $S \subset {R^3}$ be such that $S \subset \operatorname {cl} (C(S)),S$ not planar and $C(S)$ is connected. Then $S \subset \operatorname {cl} (\operatorname {int} S)$.

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