Topological properties of function spaces over ordinal spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00477380" target="_blank" >RIV/67985840:_____/17:00477380 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s13398-016-0354-7" target="_blank" >http://dx.doi.org/10.1007/s13398-016-0354-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-016-0354-7" target="_blank" >10.1007/s13398-016-0354-7</a>
Alternative languages
Result language
angličtina
Original language name
Topological properties of function spaces over ordinal spaces
Original language description
A topological space X is said to be an Ascoli space if any compact subset K of Ck(Y) is evenly continuous. This definition is motivated by the classical Ascoli theorem. We study the kR-property and the Ascoli property of Cp(k) and Ck(k) over ordinals k. We prove that Cp(k) is always an Ascoli space, while Cp(k) is a kR-space iff the cofinality of k is countable. In particular, this provides the first Cp-example of an Ascoli space which is not a kR-space, namely Cp(omega 1). We show that Ck(k) is Ascoli iff cf(k) is countable iff Ck(k) is metrizable.
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
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
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
111
Issue of the periodical within the volume
4
Country of publishing house
ES - SPAIN
Number of pages
5
Pages from-to
1157-1161
UT code for WoS article
000408424900018
EID of the result in the Scopus database
2-s2.0-85028409348