Rich families and elementary submodels

• Autorzy: Marek Cúth , Ondřej Kalenda
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Elementary submodel; Separable reduction; Projectional skeleton; Rich family

Kategorie tematyczne

• 03C30: Other model constructions
• 46B26: Nonseparable Banach spaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 7
• Strony: 1026-1039

Daty

wydano

2014-07-01

online

2014-04-03

Twórcy

autor

Marek Cúth

• Charles University

autor

Ondřej Kalenda

• Charles University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0400-z