The spaces \(C_ p(X):\) decomposition into a countable union of bounded subspaces and completeness properties

DOI10.1016/0166-8641(86)90023-4zbMath0596.54015OpenAlexW2033370617MaRDI QIDQ1078848

Vladimir V. Tkachuk

Publication date: 1986

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(86)90023-4

zbMATH Keywords

Baire spacestopology of pointwise convergencebounded subset\(\omega \) - discrete space\(\sigma \) -bounded space\(\sigma \) -pseudocompact space\(C_{\infty }\)-discrete spaceb-discrete spacepseudocompleteness

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Baire category, Baire spaces (54E52) Realcompactness and realcompactification (54D60) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25)

Related Items (22)

A selection of recent results and problems in \(C_{p}\)-theory ⋮ Final compactness is not preserved under products of spaces of the form \(C_ p(X)\) ⋮ Algebraic objects generated by topological structure ⋮ Covering properties of Cp(X) and Ck(X) ⋮ Pseudo-completeness of the compact-open topology on \(C(X)\) ⋮ Weak pseudocompactness on spaces of continuous functions ⋮ Properties of function spaces reflected by uniformly dense subspaces. ⋮ On the \(\sigma\)-countable compactness of spaces of continuous functions with the set-open topology ⋮ Remainders of products, topological groups and \(C_p\)-spaces ⋮ Completeness type properties on \(C_{p}(X,Y)\) spaces ⋮ The projective Menger property and an embedding of \(S_{\omega}\) into function spaces ⋮ Chain conditions and continuous mappings on \(C_ p(X)\) ⋮ Completeness and compactness properties in metric spaces, topological groups and function spaces ⋮ On compact weaker topologies in function spaces ⋮ On weakly compact sets in \(C\left( X\right) \) ⋮ There is no domain representable dense proper subsemigroup of a topological group ⋮ Methods of the theory of cardinal invariants and the theory of mappings as applied to spaces of functions ⋮ Basic and Classic Results on Pseudocompact Spaces ⋮ Weakly Pseudocompact Spaces ⋮ Some results on separate and joint continuity ⋮ Some observations on \(C_p\)-theory and bibliography ⋮ Special issue on \(C_p(X)\)-theory

Cites Work

• Category in function spaces. I
• Pseudo-completeness and the product of Baire spaces
• Cartesian products of Baire spaces
• Examples of connected left-separated spaces and topological groups
• The Density Character of Function Spaces
• Ascoli theorems and the pseudocharacter of mapping spaces
• Partial Orders on the Types in βN
• Criteres de Compacite dans les Espaces Fonctionnels Generaux
• TOPOLOGICAL VECTOR SPACES OF CONTINUOUS FUNCTIONS
• On locally convex vector spaces of continuous functions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The spaces \(C_ p(X):\) decomposition into a countable union of bounded subspaces and completeness properties