Metrization conditions for topological vector spaces with Baire type properties

S. S. Gabriyelyan; J. Ka̧kol

doi:10.1016/j.topol.2014.05.007

Metrization conditions for topological vector spaces with Baire type properties

S. S. Gabriyelyan, J. Ka̧kol

Department of Mathematics

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

Abstract

We show: (i) A Baire topological vector space is metrizable if and only if it has countable c^{s *}-character. (ii) A locally convex b-Baire-like space is metrizable if and only if it has countable c^{s *}-character. Both results extend earlier metrization theorems involving the concept of the c^{s *}-countable character. Theorem (ii) extends a theorem (Sakai) stating that the space _{C p}(X) has countable c^{s *}-character if and only if X is countable.

Original language	American English
Pages (from-to)	135-141
Number of pages	7
Journal	Topology and its Applications
Volume	173
DOIs	https://doi.org/10.1016/j.topol.2014.05.007
State	Published - 15 Aug 2014

Keywords

B-Baire-like space
Baire space
Locally convex space
Metric space
Topological vector space

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1016/j.topol.2014.05.007

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title = "Metrization conditions for topological vector spaces with Baire type properties",

abstract = "We show: (i) A Baire topological vector space is metrizable if and only if it has countable cs *-character. (ii) A locally convex b-Baire-like space is metrizable if and only if it has countable cs *-character. Both results extend earlier metrization theorems involving the concept of the cs *-countable character. Theorem (ii) extends a theorem (Sakai) stating that the space C p(X) has countable cs *-character if and only if X is countable.",

keywords = "B-Baire-like space, Baire space, Locally convex space, Metric space, Topological vector space",

author = "Gabriyelyan, \{S. S.\} and J. K{\c a}kol",

note = "Funding Information: Research supported by National Center of Science , Poland, grant no. N N201 605340 and also by Generalitat Valenciana , Conselleria d'Educaci{\'o}, Cultura i Esport, Spain, Grant PROMETEO/2013/058 .",

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doi = "10.1016/j.topol.2014.05.007",

language = "American English",

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journal = "Topology and its Applications",

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TY - JOUR

T1 - Metrization conditions for topological vector spaces with Baire type properties

AU - Gabriyelyan, S. S.

AU - Ka̧kol, J.

N1 - Funding Information: Research supported by National Center of Science , Poland, grant no. N N201 605340 and also by Generalitat Valenciana , Conselleria d'Educació, Cultura i Esport, Spain, Grant PROMETEO/2013/058 .

PY - 2014/8/15

Y1 - 2014/8/15

N2 - We show: (i) A Baire topological vector space is metrizable if and only if it has countable cs *-character. (ii) A locally convex b-Baire-like space is metrizable if and only if it has countable cs *-character. Both results extend earlier metrization theorems involving the concept of the cs *-countable character. Theorem (ii) extends a theorem (Sakai) stating that the space C p(X) has countable cs *-character if and only if X is countable.

AB - We show: (i) A Baire topological vector space is metrizable if and only if it has countable cs *-character. (ii) A locally convex b-Baire-like space is metrizable if and only if it has countable cs *-character. Both results extend earlier metrization theorems involving the concept of the cs *-countable character. Theorem (ii) extends a theorem (Sakai) stating that the space C p(X) has countable cs *-character if and only if X is countable.

KW - B-Baire-like space

KW - Baire space

KW - Locally convex space

KW - Metric space

KW - Topological vector space

UR - http://www.scopus.com/inward/record.url?scp=84901610800&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2014.05.007

DO - 10.1016/j.topol.2014.05.007

M3 - Article

SN - 0166-8641

VL - 173

SP - 135

EP - 141

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Metrization conditions for topological vector spaces with Baire type properties

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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