On spaces Cb(X) weakly K-analytic

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00480815" target="_blank" >RIV/67985840:_____/17:00480815 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/mana.201600406" target="_blank" >http://dx.doi.org/10.1002/mana.201600406</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201600406" target="_blank" >10.1002/mana.201600406</a>

Result language
angličtina
Original language name
On spaces Cb(X) weakly K-analytic
Original language description
A subset Y of the dual closed unit ball BE* of a Banach space E is called a Rainwater set for E if every bounded sequence of E that converges pointwise on Y converges weakly in E. In this paper, topological properties of Rainwater sets for the Banach space Cb(X) of the real-valued continuous and bounded functions defined on a completely regular space X equipped with the supremum-norm are studied. This applies to characterize the weak K-analyticity of Cb(X) in terms of certain Rainwater sets for Cb(X). Particularly, we show that Cb(X) is weakly K-analytic if and only if there exists a Rainwater set Y for Cb(X) such that Cb(X),omegaY is both K-analytic and angelic, where omegaY denotes the topology on Cb(X) of the pointwise convergence on Y. For the case when X is compact, one gets classic Talagrand's theorem.
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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