%0 Journal Article
%T On Separable Determination of Sigma-P-Porous Sets in Banach Spaces
%A Marek Cuth
%A Martin Rmoutil
%A Miroslav Zeleny
%J Mathematics
%D 2013
%I arXiv
%R 10.1016/j.topol.2014.11.005
%X 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.
%U http://arxiv.org/abs/1309.2174v1