Rich families and elementary submodels

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10210855" target="_blank" >RIV/00216208:11320/14:10210855 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.2478/s11533-013-0400-z" target="_blank" >http://dx.doi.org/10.2478/s11533-013-0400-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.2478/s11533-013-0400-z" target="_blank" >10.2478/s11533-013-0400-z</a>

Result language
angličtina
Original language name
Rich families and elementary submodels
Original language description
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 aleph_1. 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 generalityindexed by ranges of its projections.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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