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

0542588 - MÚ 2022 RIV US eng J - Článek v odborném periodiku
Kąkol, Jerzy - Leiderman, A. G.
A characterization of X for which spaces C_p(X) are distinguished and applications.
Proceedings of the American Mathematical Society, Ser. B. Roč. 8, February (2021), s. 86-99. E-ISSN 2330-1511
Grant CEP: GA ČR(CZ) GF20-22230L
Institucionální podpora: RVO:67985840
Klíčová slova: distinguished locally convex space * scattered compact space * delta-set * Isbell–Mrówka space
Obor OECD: Pure mathematics
Způsob publikování: Open access
https://doi.org/10.1090/bproc/76

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.
Trvalý link: http://hdl.handle.net/11104/0319974