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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

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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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