On points at which a set is cone-shaped

Authors:
M. Edelstein, L. Keener and R. O’Brien

Journal:
Proc. Amer. Math. Soc. **66** (1977), 327-330

MSC:
Primary 46B05; Secondary 52A05

DOI:
https://doi.org/10.1090/S0002-9939-1977-0454593-6

MathSciNet review:
0454593

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Abstract: A set in a normed linear space *X* is said to be cone-shaped at if there is a closed half-space that has *x* in its bounding hyperplane and contains . The point *x* is called a cone point. In this paper it is shown that if *X* has an equivalent uniformly convex and uniformly smooth norm and if is a closed bounded subset with the finite visibility property for cone points (i.e., for every finite set *F* of cone points of *S* there is a point such that for all ), then *S* is starshaped.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0454593-6

Keywords:
Starshaped,
superreflexive,
finite visibility

Article copyright:
© Copyright 1977
American Mathematical Society