Distinguished \(C_p (X)\) spaces

DOI10.1007/s13398-020-00967-4zbMath1460.54011OpenAlexW3107843551MaRDI QIDQ2220963

Jerzy Kąkol, Stephen A. Saxon, Arkady G. Leiderman, Juan Carlos Ferrando

Publication date: 25 January 2021

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-020-00967-4

zbMATH Keywords

Fréchet spacebidual spacedistinguished spaceEberlein compact spacestrongly splittable space

Mathematics Subject Classification ID

Function spaces in general topology (54C35) General theory of locally convex spaces (46A03) Manifolds of mappings (58D15)

Related Items (14)

Bounded resolutions for spaces \(C_p(X)\) and a characterization in terms of \(X\) ⋮ \(\omega^{\omega}\)-base and infinite-dimensional compact sets in locally convex spaces ⋮ Approximation by pointwise bounded sets of continuous functions ⋮ Feral dual spaces and (strongly) distinguished spaces \(C(X)\) ⋮ Distinguished \(C_p(X)\) spaces and the strongest locally convex topology ⋮ On Asplund spaces \(C_k(X)\) and \(w^*\)-binormality ⋮ 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 ⋮ A note on the weak topology of spaces \(C_k(X)\) of continuous functions ⋮ If not distinguished, is $C_{p}( X) $ even close? ⋮ Distinguished vector-valued continuous function spaces and injective tensor products ⋮ A characterization of $X$ for which spaces $C_p(X)$ are distinguished and its applications ⋮ Pseudocompact \(\Delta\)-spaces are often scattered

Cites Work

• The dual of the locally convex space \(C_p(X)\)
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• On scattered Eberlein compact spaces
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• Dual density conditions in (DF)-spaces. I
• Weak topology of spaces of continuous functions
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• A \(C_p\)-theory problem book. Compactness in function spaces
• Weak compactness and metrizability of Mackey$^*$-bounded sets in Fréchet spaces
• A \(C_p\)-theory problem book. Special features of function spaces
• A characterization of distinguished Fréchet spaces
• Ultrapowers of Locally Convex Spaces and Applications, I
• Examples of non-distinguished Fréchet spaces
• Barrelled spaces and dense vector subspaces
• Hereditary m-separability and the hereditary m-Lindelöf property in product spaces and function spaces
• On some subspaces of the Helly space
• Some remarks on Eberlein compacts
• Optimal Cardinals for Metrizable Barrelled Spaces
• The fit and flat components of barrelled spaces
• Bounded sets structure of CpX and quasi‐(DF)‐spaces
• Cardinality of a space containing a dense part of a given cardinality
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