Uniform Eberlein spaces and the finite axiom of choice
| dc.creator | Morillon, Marianne | |
| dc.date | 2008-04-01 | |
| dc.date.accessioned | 2026-07-07T12:18:02Z | |
| dc.date.available | 2026-07-07T12:18:02Z | |
| dc.description | We work in set-theory without choice $\ZF$. Given a closed subset $F$ of $[0,1]^I$ which is a bounded subset of $\ell^1(I)$ ({\em resp.} such that $F \subseteq \ell^0(I)$), we show that the countable axiom of choice for finite subsets of $I$, ({\em resp.} the countable axiom of choice $\ACD$) implies that $F$ is compact. This enhances previous results where $\ACD$ ({\em resp.} the axiom of Dependent Choices $\DC$) was required. Moreover, if $I$ is linearly orderable (for example $I=\IR$), the closed unit ball of $\ell^2(I)$ is weakly compact (in $\ZF$). | |
| dc.identifier | https://arxiv.org/abs/0804.0154 | |
| dc.identifier | http://arxiv.org/abs/0804.0154 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212274 | |
| dc.subject | Functional Analysis | |
| dc.subject | General Topology | |
| dc.subject | Logic | |
| dc.subject | 03E25, 54B10, 54D30, 46B26 | |
| dc.title | Uniform Eberlein spaces and the finite axiom of choice | |
| dc.type | text |