Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 0454593
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A set $ \mathcal{S}$ in a normed linear space X is said to be cone-shaped at $ x \in X$ if there is a closed half-space that has x in its bounding hyperplane and contains $ \{ y \in \mathcal{S}:[x,y] \subset S\} $. 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 $ \mathcal{S}$ 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 $ z \in S$ such that $ [z,y] \subset \mathcal{S}$ for all $ y \in F$), then S is starshaped.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B05, 52A05

Retrieve articles in all journals with MSC: 46B05, 52A05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0454593-6
PII: S 0002-9939(1977)0454593-6
Keywords: Starshaped, superreflexive, finite visibility
Article copyright: © Copyright 1977 American Mathematical Society