A characterization of X for which spaces C_p(X) are distinguished and applications

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00542588" target="_blank" >RIV/67985840:_____/21:00542588 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/bproc/76" target="_blank" >https://doi.org/10.1090/bproc/76</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/bproc/76" target="_blank" >10.1090/bproc/76</a>

Result language
angličtina
Original language name
A characterization of X for which spaces C_p(X) are distinguished and applications
Original language description
We prove that the locally convex space of continuous real-valued functions on a Tychonoff space equipped with the topology of pointwise convergence is distinguished if and only if is a -space in the sense of Knight in [Trans. Amer. Math. Soc. 339 (1993), pp. 45–60]. As an application of this characterization theorem we obtain the following results: [1)] If is a Čech-complete (in particular, compact) space such that is distinguished, then is scattered. [2)] For every separable compact space of the Isbell–Mrówka type , the space is distinguished. [3)] If is the compact space of ordinals , then is not distinguished. We observe that the existence of an uncountable separable metrizable space such that is distinguished, is independent of ZFC. We also explore the question to which extent the class of -spaces is invariant under basic topological operations.
Czech name
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Czech description
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Project
<a href="/en/project/GF20-22230L" target="_blank" >GF20-22230L: Banach spaces of continuous and Lipschitz functions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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