Cp-spaces dominated by metrizable topologies

0507735 - MÚ 2020 RIV NL eng J - Článek v odborném periodiku
Kąkol, Jerzy
Cp-spaces dominated by metrizable topologies.
Topology and its Applications. Roč. 265, 15 September (2019), č. článku 106837. ISSN 0166-8641. E-ISSN 1879-3207
Institucionální podpora: RVO:67985840
Klíčová slova: Fréchet space * function space * hemicompact space
Obor OECD: Pure mathematics
Impakt faktor: 0.531, rok: 2019
Způsob publikování: Omezený přístup
http://dx.doi.org/10.1016/j.topol.2019.106837

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.
Trvalý link: http://hdl.handle.net/11104/0298711