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A generalization of Tietze's theorem on convex sets in $ R\sp{3}$


Author: Nick M. Stavrakas
Journal: Proc. Amer. Math. Soc. 40 (1973), 565-567
MSC: Primary 52A15
DOI: https://doi.org/10.1090/S0002-9939-1973-0341280-4
MathSciNet review: 0341280
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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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DOI: https://doi.org/10.1090/S0002-9939-1973-0341280-4
Article copyright: © Copyright 1973 American Mathematical Society

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