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COMPATIBLE LOCALLY CONVEX TOPOLOGIES ON NORMED SPACES: CARDINALITY ASPECTS

Part of: Normed linear spaces and Banach spaces; Banach lattices Topological linear spaces and related structures

Published online by Cambridge University Press:  13 March 2017

ELENA MARTÍN-PEINADOR ,
ANATOLIJ PLICHKO  and
VAJA TARIELADZE
ELENA MARTÍN-PEINADOR*
Affiliation:
Instituto de Matemática Interdisciplinar yDepartamento de Geometría y Topología, Universidad Complutense de Madrid, 28040 Madrid, Spain email em_peinador@mat.ucm.es
ANATOLIJ PLICHKO
Affiliation:
Institute of Mathematics, Cracow University of Technology, 31-155 Cracow, Poland email aplichko@pk.edu.pl
VAJA TARIELADZE
Affiliation:
Niko Muskhelishvili Institute of Computational Mathematics of the Georgian Technical University, 0175 Tbilisi, Georgia email vajatarieladze@yahoo.com
*
✉em_peinador@mat.ucm.es
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Abstract

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For a normed infinite-dimensional space, we prove that the family of all locally convex topologies which are compatible with the original norm topology has cardinality greater or equal to $\mathfrak{c}$.

Keywords

normed spacelocally convex topologycompatible topologycardinalityantichain

MSC classification

Primary: 46A03: General theory of locally convex spaces
Secondary: 46A20: Duality theory 46B10: Duality and reflexivity 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 1 , August 2017 , pp. 139 - 145
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author was partially supported by the Spanish Ministerio de Economía y Competitividad, projects MTM 2013-42486-P and MTM 2016-79422-P. The third author was supported by the Shota Rustaveli National Science Foundation, grant no. FR/539/5-100/13.

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