Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496009 | Journal of Functional Analysis | 2005 | 25 Pages |
Abstract
The concept of continuous set has been used in finite dimension by Gale and Klee and recently by Auslender and Coutat. Here, we introduce the notion of slice-continuous set in a reflexive Banach space and we show that the class of such sets can be viewed as a subclass of the class of continuous sets. Further, we prove that every nonconstant real-valued convex and continuous function, which has a global minima, attains its infimum on every nonempty convex and closed subset of a reflexive Banach space if and only if its nonempty level sets are slice-continuous. Thereafter, we provide a new separation property for closed convex sets, in terms of slice-continuity, and conclude this article by comments.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Emil Ernst, Michel Théra, Constantin ZÄlinescu,