On metrizable subspaces and quotients of non-Archimedean spaces Cp(X,K)
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00524453" target="_blank" >RIV/67985840:_____/20:00524453 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13398-020-00849-9" target="_blank" >https://doi.org/10.1007/s13398-020-00849-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-020-00849-9" target="_blank" >10.1007/s13398-020-00849-9</a>
Alternative languages
Result language
angličtina
Original language name
On metrizable subspaces and quotients of non-Archimedean spaces Cp(X,K)
Original language description
We show that for any X [with an infinite compact subset] the space Cp(X,K) has an infinite-dimensional [closed] metrizable subspace isomorphic to c0(N,K). Next we prove that Cp(X,K) has a quotient isomorphic to c0(N,K) if and only if it has a complemented subspace isomorphic to c0(N,K). It follows that for any extremally disconnected compact space X the space Cp(X,K) has no quotient isomorphic to the space c0(N,K), in particular, for any infinite discrete space D the space Cp(βD,K) has no quotient isomorphic c0(N,K). Finally we investigate the question for which X the spaceCp(X,K) has an infinite-dimensionalmetrizable quotient.
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/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales
ISSN
1578-7303
e-ISSN
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Volume of the periodical
114
Issue of the periodical within the volume
3
Country of publishing house
ES - SPAIN
Number of pages
23
Pages from-to
125
UT code for WoS article
000531012700001
EID of the result in the Scopus database
2-s2.0-85084256848