Metric spaces with the small ball property (Q2773405)
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: Metric spaces with the small ball property |
scientific article; zbMATH DE number 1709996
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Metric spaces with the small ball property |
scientific article; zbMATH DE number 1709996 |
Statements
Metric spaces with the small ball property (English)
0 references
21 February 2002
0 references
small ball property
0 references
compact set
0 references
A metric space \(M\) has the small ball property (SBP) whenever for every \(\varepsilon > 0\) there is a cover of \(M\) by a sequence of closed balls whose radii are bounded above by \(\varepsilon\) and vanish. The authors establish a few properties of spaces with the SBP. For instance, a bounded closed convex subset \(U\) of a Banach space enjoys the SBP whenever \(U\) is compact.NEWLINENEWLINESee also: [\textit{E. Behrends}, Acknowledgement of priority, Rend. Circ. Mat. Palermo (2) 55, No. 3, 449 (2006; Zbl 1196.46014)].
0 references
