Metrizable quotients of Cp-spaces
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Metrizable quotients of Cp-spaces
Original language description
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.
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
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Topology and its Applications
ISSN
0166-8641
e-ISSN
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Volume of the periodical
249
Issue of the periodical within the volume
1 November
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
8
Pages from-to
95-102
UT code for WoS article
000449136000008
EID of the result in the Scopus database
2-s2.0-85053511144