The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces

DOI10.4064/sm8289-4-2016zbMath1354.46004arXiv1504.04202OpenAlexW2963516897MaRDI QIDQ2809358

Jerzy Kąkol, Grzegorz Plebanek, Saak S. Gabriyelyan

Publication date: 27 May 2016

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.04202

zbMATH Keywords

weak topologyBanach spaceFréchet spacetopological spaceAscoli space

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Locally convex Fréchet spaces and (DF)-spaces (46A04) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15) Compactness in topological linear spaces; angelic spaces, etc. (46A50)

Related Items (18)

On the \(C_k\)-stable closure of the class of (separable) metrizable spaces ⋮ Topological properties of function spaces \(C_{k}(X,2)\) over zero-dimensional metric spaces \(X\) ⋮ On the separable quotient problem for Banach spaces ⋮ The Ascoli property for function spaces ⋮ On the weak and pointwise topologies in function spaces. II. ⋮ On the Ascoli property for locally convex spaces ⋮ Descriptive topology for analysts ⋮ Topological properties of function spaces over ordinals ⋮ A topological group observation on the Banach-Mazur separable quotient problem ⋮ On reflexivity and the Ascoli property for free locally convex spaces ⋮ Topological properties of strict (\textit{LF})-spaces and strong duals of Montel strict (\textit{LF})-spaces ⋮ On bounded sets in \(C_k ( X )\) ⋮ Ascoli and sequentially Ascoli spaces ⋮ Topological properties of inductive limits of closed towers of metrizable groups ⋮ Ascoli's theorem for pseudocompact spaces ⋮ Topological properties of spaces of Baire functions ⋮ Locally convex properties of free locally convex spaces ⋮ A note on Banach spaces \(E\) for which \(E_w\) is homeomorphic to \(C_p(X)\)

Cites Work

• On the \(C_k\)-stable closure of the class of (separable) metrizable spaces
• Topological properties of Banach spaces
• On stratifiable spaces
• The Weak Topology of a Banach Space
• Frechet Spaces with Nuclear Kothe Quotients
• Unnamed Item
• Unnamed Item

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