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
participants (1)
-
alspach@math.okstate.edu