Projective versions of selection principles

DOI10.1016/j.topol.2009.12.004zbMath1189.54016OpenAlexW2013212215MaRDI QIDQ2268842

Maddalena Bonanzinga, Filippo Cammaroto, Mikhail V. Matveyev

Publication date: 9 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.topol.2009.12.004

zbMATH Keywords

Fréchet spaceprojectively Hurewiczprojectively Mengerprojectively \(\gamma\)-spaceprojectively Rothbergerweakly Fréchet space

Mathematics Subject Classification ID

Continuous maps (54C05) Function spaces in general topology (54C35) Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20)

Related Items

Classification of selectors for sequences of dense sets of \(C_{p}(X)\), Dowker-type example and Arhangelskii's \(\alpha_2\)-property, Indestructibility of compact spaces, Productively Lindelöf and indestructibly Lindelöf spaces, Further applications of bornological covering properties in function spaces, Projective versions of the properties in the Scheepers diagram, On embedding of F-hedgehogs in function spaces, Productive Lindelöfness and a class of spaces considered by Z. Frolík, The Menger property and \(l\)-equivalence, Remarks on the Menger property of \(C_{p}(X,2)\), Application of selection principles in the study of the properties of function spaces, The projective Menger property and an embedding of \(S_{\omega}\) into function spaces, Rothberger bounded groups and Ramsey theory, Strongly sequentially separable function spaces, via selection principles, Game-theoretical aspects of the Borel conjecture, On the Menger and almost Menger properties in locales

Cites Work

• Function spaces and a property of Reznichenko
• The sequence selection properties of \(C_p(X)\)
• A consistent \(\sigma\)-compact sequential space which is not hereditarily weakly Whyburn
• When does the Haver property imply selective screenability?
• Precalibers, monolithic spaces, first countability, and homogeneity in the class of compact spaces
• The combinatorics of the Baer-Specker group
• Spaces \(N\cup\mathcal R\) and their dimensions
• Some properties of C(X). I
• Spaces not distinguishing pointwise and quasinormal convergence of real functions
• Generalizations of the first axiom of countability
• On the consistency of Borel's conjecture
• \(C_p(X)\) and Arhangel'skiĭ's \(\alpha_i\)-spaces
• Projective \(\sigma\)-compactness, \(\omega_1\)-caliber, and \(C_p\)-spaces
• Some properties of C(X). II
• Combinatorics of open covers. VIII
• 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]
• Continuous Functions on Compact Spaces Without Perfect Subsets
• On Properties Characterizing Pseudo-Compact Spaces
• Spaces of continuous functions (III) (Spaces C(Ω) for Ω without perfect subsets)
• Metrizabillity of certain quotient space
• Selective screenability and the Hurewicz property
• A metric space with the Haver property whose square fails this property
• Partition Algebras for Almost-Disjoint Families
• Function spaces in the topology of pointwise convergence, and compact sets
• On some properties of Hurewicz, Menger, and Rothberger
• Some Properties of Measure and Category
• Normal P-spaces and the $G_δ $-topology
• A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandrof's problem
• A sequential property of $\mathsf {C}_p(X)$ and a covering property of Hurewicz
• The algebraic sum of sets of real numbers with strong measure zero sets
• Combinatorics of open covers (VII): Groupability
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