Measure of non-compactness and multivalued mappings in complete metric topological vector spaces (Q1072157)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Measure of non-compactness and multivalued mappings in complete metric topological vector spaces |
scientific article; zbMATH DE number 3942491
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Measure of non-compactness and multivalued mappings in complete metric topological vector spaces |
scientific article; zbMATH DE number 3942491 |
Statements
Measure of non-compactness and multivalued mappings in complete metric topological vector spaces (English)
0 references
1985
0 references
The author generalizes a theorem of Kuratowski to the following: In a complete metric space any family \(\{\) \(F\}\) of closed subsets having the finite intersection property and for which inf \(\alpha\) (F)\(=0\), has a non-empty compact intersection, where \(\alpha\) (F) is the measure of non- compactness of F. He then applies this result to KKM set-valued maps introduced by \textit{J. Dugundji} and \textit{A. Granas} [Ann. Sc. Norm. Sup. Pisa, Cl. Sci., IV. Ser. 5, 679-682 (1978; Zbl 0396.47037)].
0 references
complete metric space
0 references
measure of non-compactness
0 references
KKM set-valued maps
0 references
