Metrizable bounded sets in C(X) spaces and distinguished Cp(X) spaces

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

Metrizable bounded sets in C(X) spaces and distinguished Cp(X) spaces

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Metrizable bounded sets in C(X) spaces and distinguished Cp(X) spaces

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF16-34860L" target="_blank" >GF16-34860L: Logika a topologie v Banachových prostorech</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Svazek periodika

26

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

10

Strana od-do

1337-1346

Kód UT WoS článku

000495892000015

EID výsledku v databázi Scopus

2-s2.0-85068964405