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σ -porosity is separably determined

Marek Cúth, Martin Rmoutil (2013)

Czechoslovak Mathematical Journal

We prove a separable reduction theorem for σ -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 σ -porous in X if and only if A V is σ -porous in V . Such a result is proved for several types of σ -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...

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