Metrizable bounded sets in C(X) spaces and distinguished Cp(X) spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00510255" target="_blank" >RIV/67985840:_____/19:00510255 - isvavai.cz</a>
Result on the web
<a href="http://www.heldermann.de/JCA/JCA26/JCA264/jca26070.htm" target="_blank" >http://www.heldermann.de/JCA/JCA26/JCA264/jca26070.htm</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Metrizable bounded sets in C(X) spaces and distinguished Cp(X) spaces
Original language description
Quite recently W. Ruess [17] has shown that a wide class of locally convex spaces for which all bounded sets are metrizable enjoy Rosenthal's ∂1-dichotomy. Being motivated by this fact we show that for a Tychonoff space X the bounded sets of Cp (X) are metrizable (respectively, the bounded sets of Ck (X) are weakly metrizable) if and only if X is countable. If X is a P-space we show that every bounded set in Cp (X) is metrizable if and only if X is countable and discrete. The second part of the paper deals with distinguished Cp (X) spaces. Among other things we show that Cp (X) is distinguished if and only if the strong topology of the dual coincides with its strongest locally convex topology, and that Cp (X) is always distinguished whenever X is countable.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GF16-34860L" target="_blank" >GF16-34860L: Logic and Topology in Banach spaces</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Convex Analysis
ISSN
0944-6532
e-ISSN
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Volume of the periodical
26
Issue of the periodical within the volume
4
Country of publishing house
DE - GERMANY
Number of pages
10
Pages from-to
1337-1346
UT code for WoS article
000495892000015
EID of the result in the Scopus database
2-s2.0-85068964405