Two properties of \(C_{p}(x)\) weaker than the Fréchet Urysohn property

DOI10.1016/j.topol.2005.11.012zbMath1100.54011OpenAlexW2095181512MaRDI QIDQ2502934

Masami Sakai

Publication date: 13 September 2006

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

Full work available at URL: https://doi.org/10.1016/j.topol.2005.11.012

zbMATH Keywords

topology of pointwise convergencefunction space\(\omega\)-cover\(\lambda\)-space\(\kappa\)-Fréchet Urysohn property\(\omega\)-grouping property.always first categoryFréchet Urysohn propertyproperty \(\kappa\)weakly Fréchet Urysohn property

Mathematics Subject Classification ID

Function spaces in general topology (54C35) Baire category, Baire spaces (54E52) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05)

Related Items

The Ascoli property for function spaces, \(\kappa\)-Fréchet Urysohn property of \(C_{k}(X)\), Topological properties of function spaces over ordinals, Some classes of topological spaces extending the class of Δ-spaces, Ascoli and sequentially Ascoli spaces, Variations on a theorem of Arhangel'skii and Pytkeev, A note on \(\kappa\)-Fréchet-Urysohn property in function spaces, Metrization conditions for topological vector spaces with Baire type properties, Function spaces with a countable \(cs^*\)-network at a point, On the length of chains of proper subgroups covering a topological group, On the Pytkeev property in spaces of continuous functions, A selective bitopological version of the Reznichenko property in function spaces, Sequences of semicontinuous functions accompanying continuous functions, Topological properties of spaces of Baire functions, Combinatorial images of sets of reals and semifilter trichotomy

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Function spaces and a property of Reznichenko
• \(\gamma\)-sets and other singular sets of real numbers
• A pseudocompact Tychonoff space all countable subsets of which are closed and \(C^*\)-embedded
• Baire property of spaces of continuous functions
• Some properties of C(X). I
• Weakly Fréchet-Urysohn and Pytkeev spaces
• Some properties of C(X). II
• The minimal cardinality where the Reznichenko property fails
• A countable \(X\) having a closed subspace \(A\) with \(C_ p(A)\) not a factor of \(C_ p(X)\)
• On some properties of Hurewicz, Menger, and Rothberger
• Compacts de fonctions mesurables et filtres non mesurables
• ON $ \kappa$-METRIZABLE SPACE
• On Topological Classification of Function Spaces C p (X) of Low Borel Complexity
• The Pytkeev property and the Reznichenko property in function spaces