On Separable Determination of Sigma-P-Porous Sets in Banach Spaces
Functional Analysis
2014-11-26 v1
Abstract
We use a method involving elementary submodels and a partial converse of Foran lemma to prove separable reduction theorems concerning Suslin sigma-P-porous sets where "P" can be from a rather wide class of porosity-like relations in complete metric spaces. In particular, we separably reduce the notion of Suslin cone small set in Asplund spaces. As an application we prove a theorem stating that a continuous approximately convex function on an Asplund space is Frechet differentiable up to a cone small set.
Keywords
Cite
@article{arxiv.1309.2174,
title = {On Separable Determination of Sigma-P-Porous Sets in Banach Spaces},
author = {Marek Cuth and Martin Rmoutil and Miroslav Zeleny},
journal= {arXiv preprint arXiv:1309.2174},
year = {2014}
}