Abstract
We prove that the set of all support points of a nonempty closed convex bounded set C in a real infinite-dimensional Banach space X is AR(sigma-compact) and contractible. Under suitable conditions, similar results are proved also for the set of all support functionals ofC and for the domain, the graph, and the range of the subdifferential map of a proper convex lower semicontinuous function on X.
| Original language | English |
|---|---|
| Pages (from-to) | 1236-1254 |
| Number of pages | 19 |
| Journal | CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES |
| Volume | 65 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2013 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- Absolute retract
- Convex set
- Leray-Schauder continuation principle
- Mathematics (all)
- Support functional
- Support point
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