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Description
  • 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 $A\cap V$ 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 of L. Zajíček on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting.
  • 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 $A\cap V$ 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 of L. Zajíček on differentiability of Lipschitz functions on separable Asplund spaces to the nonseparable setting. (en)
Title
  • σ-porosity is separably determined
  • σ-porosity is separably determined (en)
skos:prefLabel
  • σ-porosity is separably determined
  • σ-porosity is separably determined (en)
skos:notation
  • RIV/00216208:11320/13:10159050!RIV14-MSM-11320___
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  • S
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  • 63
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  • 119578
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  • RIV/00216208:11320/13:10159050
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  • σ-porous set; porous set; separable reduction; elementary submodel (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [8C78C8E2F38D]
http://linked.open...i/riv/nazevZdroje
  • Czechoslovak Mathematical Journal
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  • 2013
http://linked.open...iv/tvurceVysledku
  • Rmoutil, Martin
  • Cúth, Marek
http://linked.open...ain/vavai/riv/wos
  • 000316756300015
issn
  • 0011-4642
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/s10587-013-0015-3
http://localhost/t...ganizacniJednotka
  • 11320
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