1. $\sigma $-porosity is separably determined
- Creator:
- Cúth, Marek and Rmoutil, Martin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- elementary submodel, separable reduction, porous set, and $\sigma $-porous set
- Language:
- English
- Description:
- 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 $A\cap V$ 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. Zajíček on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public