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arXiv · 1309.2174

On Separable Determination of Sigma-P-Porous Sets in Banach Spaces

Marek Cuth·Martin Rmoutil·Miroslav Zeleny
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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.

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Marek Cuth, Martin Rmoutil, Miroslav Zeleny. 2013-09-09. On Separable Determination of Sigma-P-Porous Sets in Banach Spaces. https://doi.org/10.1016/j.topol.2014.11.005

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