$\sigma$-porosity is separably determined

Cúth, Marek, and Rmoutil, Martin. "$\sigma $-porosity is separably determined." Czechoslovak Mathematical Journal 63.1 (2013): 219-234. <http://eudml.org/doc/252461>.

@article{Cúth2013,
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 $A\cap V$ 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.},
author = {Cúth, Marek, Rmoutil, Martin},
journal = {Czechoslovak Mathematical Journal},
keywords = {elementary submodel; separable reduction; porous set; $\sigma $-porous set; -porous set; separable reduction; elementary submodel},
language = {eng},
number = {1},
pages = {219-234},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$\sigma $-porosity is separably determined},
url = {http://eudml.org/doc/252461},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Cúth, Marek
AU - Rmoutil, Martin
TI - $\sigma $-porosity is separably determined
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 219
EP - 234
AB - 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.
LA - eng
KW - elementary submodel; separable reduction; porous set; $\sigma $-porous set; -porous set; separable reduction; elementary submodel
UR - http://eudml.org/doc/252461
ER -