[Banach] Abstract of a paper by Marek Cuth and Martin Rmoutil

This is an announcement for the paper "Sigma-porosity is separably determined" by Marek Cuth and Martin Rmoutil.

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.

Archive classification: math.FA

Mathematics Subject Classification: 28A05, 54E35, 58C20

Submitted from: cuthm5am@karlin.mff.cuni.cz

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1112.3813

or

http://arXiv.org/abs/1112.3813