\(C_p(X)\) and Arhangel'skiĭ's \(\alpha_i\)-spaces

DOI10.1016/S0166-8641(97)00218-6zbMath0930.54017MaRDI QIDQ1295208

Marion Scheepers

Publication date: 13 September 1999

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

zbMATH Keywords

tightness\(QN\)-space

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20)

Related Items (27)

Classification of selectors for sequences of dense sets of \(C_{p}(X)\) ⋮ The functional characterizations of the Rothberger and Menger properties ⋮ The sequence selection properties of \(C_p(X)\) ⋮ A functional characterization of the Hurewicz property ⋮ QN-spaces, wQN-spaces and covering properties ⋮ More on Arhangel’skiĭ sheaf amalgamations ⋮ Convergent sequences in topological groups ⋮ Dowker-type example and Arhangelskii's \(\alpha_2\)-property ⋮ Modifications of sequence selection principles ⋮ Projective versions of the properties in the Scheepers diagram ⋮ On countably perfectly meager and countably perfectly null sets ⋮ Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations ⋮ The Ramsey property for \(C_p(X)\) ⋮ Sequence selection principles for quasi-normal convergence ⋮ Unbounded towers and products ⋮ Principle \(\mathrm{S}_1(\mathcal{P}, \mathcal{R})\): ideals and functions ⋮ The projective Menger property and an embedding of \(S_{\omega}\) into function spaces ⋮ On wQN\(_*\) and wQN\(^*\) spaces ⋮ Spaces not distinguishing convergences of real-valued functions. ⋮ Point-cofinite covers in the Laver model ⋮ Projective versions of selection principles ⋮ Selective covering properties of product spaces, II: $\gamma $ spaces ⋮ Linear $\sigma$-additivity and some applications ⋮ Invariant Ideal Axiom ⋮ On Ramsey properties, function spaces, and topological games ⋮ On Ohta-Sakai's properties of a topological space ⋮ Scheepers’ conjecture and the Scheepers diagram

Cites Work

• \(\gamma\)-sets and other singular sets of real numbers
• The product of \(<\alpha _ i>\)-spaces
• Fréchetness of inverse limits and products
• Some properties of C(X). I
• Spaces not distinguishing pointwise and quasinormal convergence of real functions
• A-sets
• Combinatorics of open covers. I: Ramsey theory
• The combinatorics of open covers. II
• [https://portal.mardi4nfdi.de/wiki/Publication:3032970 Property C � � and Function Spaces]
• Bi-quotient maps, countably bi-sequential spaces and related topics
• Sequence-covering and countably bi-quotient mappings
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