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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 12, Issue 7

Issues

Volume 13 (2015)

Rich families and elementary submodels

Marek Cúth
  • Department of Mathematical Analysis, Faculty of Mathematics and Physic, Charles University, Sokolovská 83, Praha 8, 186 75, Czech Republic
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/ Ondřej Kalenda
  • Department of Mathematical Analysis, Faculty of Mathematics and Physic, Charles University, Sokolovská 83, Praha 8, 186 75, Czech Republic
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Published Online: 2014-04-03 | DOI: https://doi.org/10.2478/s11533-013-0400-z

Abstract

We compare two methods of proving separable reduction theorems in functional analysis — the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with elementary submodels and the converse is true in spaces with fundamental minimal system and in spaces of density ℵ1. We do not know whether the converse is true in general. We apply our results to show that a projectional skeleton may be without loss of generality indexed by ranges of its projections.

MSC: 46B26; 03C30

Keywords: Elementary submodel; Separable reduction; Projectional skeleton; Rich family

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About the article

Published Online: 2014-04-03

Published in Print: 2014-07-01


Citation Information: Open Mathematics, Volume 12, Issue 7, Pages 1026–1039, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0400-z.

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