Metrizable quotients of Cp-spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00493785" target="_blank" >RIV/67985840:_____/18:00493785 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.topol.2018.09.012" target="_blank" >http://dx.doi.org/10.1016/j.topol.2018.09.012</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.topol.2018.09.012" target="_blank" >10.1016/j.topol.2018.09.012</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Metrizable quotients of Cp-spaces

Popis výsledku v původním jazyce

The famous Rosenthal–Lacey theorem asserts that for each infinite compact set K the Banach space C(K) admits a quotient which is either an isomorphic copy of c or ℓ2. What is the case when the uniform topology of C(K) is replaced by the pointwise topology? Is it true that Cp(X) always has an infinite-dimensional separable (or better metrizable) quotient? In this paper we prove that for a Tychonoff space X the function space Cp(X) has an infinite-dimensional metrizable quotient if X either contains an infinite discrete C⁎-embedded subspace or else X has a sequence (Kn)nin N of infinite compact subsets such that for every n the space Kn contains two disjoint topological copies of Kn+1. Applying the latter result, we show that under ◊ there exists a zero-dimensional Efimov space K whose function space Cp(K) has an infinite-dimensional metrizable quotient. These two theorems essentially improve earlier results of Ka̧kol and Śliwa on infinite-dimensional separable quotients of Cp-spaces.

Název v anglickém jazyce

Metrizable quotients of Cp-spaces

Popis výsledku anglicky

The famous Rosenthal–Lacey theorem asserts that for each infinite compact set K the Banach space C(K) admits a quotient which is either an isomorphic copy of c or ℓ2. What is the case when the uniform topology of C(K) is replaced by the pointwise topology? Is it true that Cp(X) always has an infinite-dimensional separable (or better metrizable) quotient? In this paper we prove that for a Tychonoff space X the function space Cp(X) has an infinite-dimensional metrizable quotient if X either contains an infinite discrete C⁎-embedded subspace or else X has a sequence (Kn)nin N of infinite compact subsets such that for every n the space Kn contains two disjoint topological copies of Kn+1. Applying the latter result, we show that under ◊ there exists a zero-dimensional Efimov space K whose function space Cp(K) has an infinite-dimensional metrizable quotient. These two theorems essentially improve earlier results of Ka̧kol and Śliwa on infinite-dimensional separable quotients of Cp-spaces.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

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

2018

Kód důvěrnosti údajů

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

Název periodika

Topology and its Applications

ISSN

0166-8641

e-ISSN

—

Svazek periodika

249

Číslo periodika v rámci svazku

1 November

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

8

Strana od-do

95-102

Kód UT WoS článku

000449136000008

EID výsledku v databázi Scopus

2-s2.0-85053511144