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

DOI10.1090/bproc/76zbMath1473.54018arXiv2011.14299OpenAlexW3131093855MaRDI QIDQ5855738

Jerzy Kąkol, Arkady G. Leiderman

Publication date: 19 March 2021

Published in: Proceedings of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.14299

zbMATH Keywords

Isbell-Mrówka spacescattered compact spacedistinguished locally convex space\( \Delta \)-set

Mathematics Subject Classification ID

Function spaces in general topology (54C35) General theory of locally convex spaces (46A03) Scattered spaces (54G12) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05)

Related Items (13)

Approximation by pointwise bounded sets of continuous functions ⋮ Feral dual spaces and (strongly) distinguished spaces \(C(X)\) ⋮ Unnamed Item ⋮ Distinguished \(C_p(X)\) spaces and the strongest locally convex topology ⋮ On Asplund spaces \(C_k(X)\) and \(w^*\)-binormality ⋮ On subspaces of spaces \(C_p(X)\) isomorphic to spaces \(c_0\) and \(\ell_q\) with the topology induced from \(\mathbb{R}^{\mathbb{N}}\) ⋮ Some classes of topological spaces extending the class of Δ-spaces ⋮ On linear continuous operators between distinguished spaces \(C_p(X)\) ⋮ Basic properties of 𝑋 for which the space 𝐶_{𝑝}(𝑋) is distinguished ⋮ Grothendieck spaces: the landscape and perspectives ⋮ If not distinguished, is $C_{p}( X) $ even close? ⋮ Distinguished vector-valued continuous function spaces and injective tensor products ⋮ Pseudocompact \(\Delta\)-spaces are often scattered

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