On the boundary of closed convex sets in $E^{n}$
Metric Geometry
2013-01-07 v1 Differential Geometry
Abstract
In this article a class of closed convex sets in the Euclidean -space which are the convex hull of their profiles is described. Thus a generalization of Krein-Milman theorem\cite{Lay:1982} to a class of closed non-compact convex sets is obtained. Sufficient and necessary conditions for convexity, affinity and starshapedness of a closed set and its boundary have been derived in terms of their boundary points.
Keywords
Cite
@article{arxiv.1301.0688,
title = {On the boundary of closed convex sets in $E^{n}$},
author = {M. Beltagy and S. Shenawy},
journal= {arXiv preprint arXiv:1301.0688},
year = {2013}
}