A characterization of X for which spaces C_p(X) are distinguished and applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00542588" target="_blank" >RIV/67985840:_____/21:00542588 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1090/bproc/76" target="_blank" >https://doi.org/10.1090/bproc/76</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/bproc/76" target="_blank" >10.1090/bproc/76</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A characterization of X for which spaces C_p(X) are distinguished and applications

Popis výsledku v původním jazyce

We prove that the locally convex space of continuous real-valued functions on a Tychonoff space equipped with the topology of pointwise convergence is distinguished if and only if is a -space in the sense of Knight in [Trans. Amer. Math. Soc. 339 (1993), pp. 45–60]. As an application of this characterization theorem we obtain the following results: [1)] If is a Čech-complete (in particular, compact) space such that is distinguished, then is scattered. [2)] For every separable compact space of the Isbell–Mrówka type , the space is distinguished. [3)] If is the compact space of ordinals , then is not distinguished. We observe that the existence of an uncountable separable metrizable space such that is distinguished, is independent of ZFC. We also explore the question to which extent the class of -spaces is invariant under basic topological operations.

Název v anglickém jazyce

A characterization of X for which spaces C_p(X) are distinguished and applications

Popis výsledku anglicky

We prove that the locally convex space of continuous real-valued functions on a Tychonoff space equipped with the topology of pointwise convergence is distinguished if and only if is a -space in the sense of Knight in [Trans. Amer. Math. Soc. 339 (1993), pp. 45–60]. As an application of this characterization theorem we obtain the following results: [1)] If is a Čech-complete (in particular, compact) space such that is distinguished, then is scattered. [2)] For every separable compact space of the Isbell–Mrówka type , the space is distinguished. [3)] If is the compact space of ordinals , then is not distinguished. We observe that the existence of an uncountable separable metrizable space such that is distinguished, is independent of ZFC. We also explore the question to which extent the class of -spaces is invariant under basic topological operations.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-22230L" target="_blank" >GF20-22230L: Banachovy prostory spojitých a lipschitzovských funkcí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the American Mathematical Society, Ser. B

ISSN

2330-1511

e-ISSN

2330-1511

Svazek periodika

8

Číslo periodika v rámci svazku

February

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

86-99

Kód UT WoS článku

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EID výsledku v databázi Scopus

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