Countable Choice and Compactness
| dc.creator | Morillon, Marianne | |
| dc.date | 2008-03-21 | |
| dc.date.accessioned | 2026-07-07T12:17:49Z | |
| dc.date.available | 2026-07-07T12:17:49Z | |
| dc.description | We work in set-theory without choice ZF. Denoting by AC(N) the countable axiom of choice, we show in ZF+AC(N) that the closed unit ball of a uniformly convex Banach space is compact in the convex topology (an alternative to the weak topology in ZF). We prove that this ball is (closely) convex-compact in the convex topology. Given a set I, a real number p greater or equal to 1 (resp. . p = 0), and some closed subset F of [0, 1]^I which is a bounded subset of l^p(I), we show that AC(N) (resp. DC, the axiom of Dependent Choices) implies the compactness of F. | |
| dc.identifier | https://arxiv.org/abs/0803.3131 | |
| dc.identifier | http://arxiv.org/abs/0803.3131 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212202 | |
| dc.subject | Functional Analysis | |
| dc.subject | General Topology | |
| dc.subject | Logic | |
| dc.subject | 03E25, 46B26, 54D30 | |
| dc.title | Countable Choice and Compactness | |
| dc.type | text |