The Ascoli property for function spaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00464468" target="_blank" >RIV/67985840:_____/16:00464468 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.topol.2016.08.026" target="_blank" >http://dx.doi.org/10.1016/j.topol.2016.08.026</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2016.08.026" target="_blank" >10.1016/j.topol.2016.08.026</a>
Alternative languages
Result language
angličtina
Original language name
The Ascoli property for function spaces
Original language description
The paper deals with Ascoli spaces Cp(X) and Ck(X) over Tychonoff spaces X. The class of Ascoli spaces X, i.e. spaces X for which any compact subset K of Ck(X) is evenly continuous, essentially includes the class of kR-spaces. First we prove that if Cp(X) is Ascoli, then it is κ-Fréchet–Urysohn. If X is cosmic, then Cp(X) is Ascoli iff it is κ-Fréchet–Urysohn. This leads to the following extension of a result of Morishita: If for a Čech-complete space X the space Cp(X) is Ascoli, then X is scattered. If X is scattered and stratifiable, then Cp(X) is an Ascoli space. Consequently: (a) If X is a complete metrizable space, then Cp(X) is Ascoli iff X is scattered. (b) If X is a Čech-complete Lindelöf space, then Cp(X) is Ascoli iff X is scattered iff Cp(X) is Fréchet–Urysohn. Moreover, we prove that for a paracompact space X of point-countable type the following conditions are equivalent: (i) X is locally compact. (ii) Ck(X) is a kR-space. (iii) Ck(X) is an Ascoli space.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
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
214
Issue of the periodical within the volume
1 December
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
16
Pages from-to
35-50
UT code for WoS article
000389391700003
EID of the result in the Scopus database
2-s2.0-84989181029