Cp-spaces dominated by metrizable topologies

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00507735" target="_blank" >RIV/67985840:_____/19:00507735 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.topol.2019.106837" target="_blank" >http://dx.doi.org/10.1016/j.topol.2019.106837</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2019.106837" target="_blank" >10.1016/j.topol.2019.106837</a>

Result language
angličtina
Original language name
Cp-spaces dominated by metrizable topologies
Original language description
Following Christensen [11] a metrizable space X is σ-compact if and only if Cp(X) is analytic, i.e. it is a continuous image of the Polish space NN. By Michael [26] the space Cp(X) is a continuous image of a separable metric space if and only if X is cosmic, and Cp(X) is an ℵ0-space if and only if X is countable. We show here that, in parallel manner, Christensen-Calbrix and Michael results may be characterized as follows: For a metrizable space X the space Cp(X) is analytic if and only if Cp(X) is a continuous linear image of a separable metrizable locally convex space, and a Tychonoff space X is a submetrizable hemicompact kR-space if and only if Cp(X) is a continuous linear image of a metrizable and complete separable locally convex space. Applications are provided.
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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