Metrizable-like locally convex topologies on C(X)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00480760" target="_blank" >RIV/67985840:_____/17:00480760 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.topol.2017.07.016" target="_blank" >http://dx.doi.org/10.1016/j.topol.2017.07.016</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.topol.2017.07.016" target="_blank" >10.1016/j.topol.2017.07.016</a>

Result language
angličtina
Original language name
Metrizable-like locally convex topologies on C(X)
Original language description
The classic Arens theorem states that the space C(X) of real-valued continuous functions on a Tychonoff space X is metrizable in the compact-open topology Tk if and only if X is hemicompact. Less demanding but still applicable problem asks whether Tk has an NN-decreasing base at zero (Ualpha)alphainNN, called in the literature a G-base. We characterize those spaces X for which C(X) admits a locally convex topology T between the pointwise topology TP and the bounded-open topology Tb such that (C(X),T) is either metrizable or is an (LM)-space or even has a G-base.
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
<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)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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