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arXiv · 1112.3813

Sigma-porosity is separably determined

Marek Cúth·Martin Rmoutil
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Abstract

We prove a separable reduction theorem for sigma-porosity of Suslin sets. In particular, if A is a Suslin subset in a Banach space X, then each separable subspace of X can be enlarged to a separable subspace V such that A is sigma-porous in X if and only if the intersection of A and V is sigma-porous in V. Such a result is proved for several types of sigma-porosity. The proof is done using the method of elementary submodels, hence the results can be combined with other separable reduction theorems. As an application we extend a theorem of L.Zajicek on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting.

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Marek Cúth, Martin Rmoutil. 2012-03-07. Sigma-porosity is separably determined. https://doi.org/10.1007/s10587-013-0015-3

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