Title: Survey on Baire-type properties in metrizable c0(Ω, X)
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-23-00005; Volume 6 / Issue 3 / Year 2024, Pages 11-15
Document Type: Research Paper
Author(s): Salvador López-Alfonso a , Manuel López-Pellicer
b , Santiago Moll-López
c
aDepartamento de Construcciones Arquitectónicas, Universitat Politècnica de València, 46022 Valencia, Spain
bIUMPA, Universitat Politècnica de València, 46022 Valencia, Spain
cDepartamento de Matemática Aplicada, Universitat Politècnica de València, 46022 Valencia, Spain
Received: 24 March 2023, Accepted: 18 May 2023, Published: 21 June 2023
Corresponding Author: Manuel López-Pellicer (Email address: mlopezpe@mat.upv.es)
Full Text: PDF
Abstract
In [6] it was proved that if is a non-empty set and
is a normed space, the normed space
is barrelled, ultrabornological or unordered Baire-like if and only if
is, respectively, barrelled, ultrabornological or unordered Baire-like. If
is a metrizable locally convex space, and
is an increasing sequence of semi-norms defining its topology,
is the metrizable locally convex space over the field
(of the real or complex numbers) of all functions
such that for each
and
the set
is finite or empty, with the topology defined by the semi-norms
,
. Also, in [10], it was proved that the metrizable
is quasi barrelled, barrelled, ultrabornological, bornological, unordered Baire-like, totally barrelled, and barrelled of class
if and only if
is, respectively, quasi barrelled, barrelled, ultrabornological, bornological, unordered Baire-like, totally barrelled, and barrelled of class
. In [14] it was proved that the metrizable
is baireled if and only if
is baireled. Two open problems are presented.
Keywords: Banach disk, Baire, Baire-like, baireled, metrizable, unordered Baire-like
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