Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures

DOI10.1090/S0002-9939-05-07997-9zbMath1137.54018arXivmath/0208224WikidataQ123124648 ScholiaQ123124648MaRDI QIDQ5705571

Tomek Bartoszynski, Boaz Tsaban

Publication date: 9 November 2005

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0208224

zbMATH Keywords

selection principleHurewicz propertyMenger propertystrong \(\gamma\)-set

Mathematics Subject Classification ID

Noncompact covering properties (paracompact, Lindelöf, etc.) (54D20) Counterexamples in general topology (54G20) Consistency and independence results in general topology (54A35)

Related Items (25)

The combinatorics of splittability ⋮ Selective covering properties of product spaces ⋮ Products of Menger spaces: A combinatorial approach ⋮ GAMES AND HEREDITARY BAIRENESS IN HYPERSPACES AND SPACES OF PROBABILITY MEASURES ⋮ Ideal approach to convergence in functional spaces ⋮ Abstract colorings, games and ultrafilters ⋮ Geometrically significant sets of measure zero ⋮ Hurewicz sets of reals without perfect subsets ⋮ Productively Lindelöf spaces and the covering property of Hurewicz ⋮ Unbounded towers and products ⋮ Scales, fields, and a problem of Hurewicz ⋮ 𝑜-bounded groups and other topological groups with strong combinatorial properties ⋮ On the definability of Menger spaces which are not \(\sigma\)-compact ⋮ Separation properties between the \(\sigma \)-compactness and Hurewicz property ⋮ Continuous selections and \(\sigma \)-spaces ⋮ A note on unbounded strongly measure zero subgroups of the Baer-Specker group ⋮ Point-cofinite covers in the Laver model ⋮ On productively Lindelöf spaces ⋮ Linear $\sigma$-additivity and some applications ⋮ The combinatorics of the Baer-Specker group ⋮ Baire category properties of some Baire type function spaces ⋮ Selection principles in the Laver, Miller, and Sacks models ⋮ Menger subsets of the Sorgenfrey line ⋮ Products of Luzin-type sets with combinatorial properties ⋮ Some covering properties in topological and uniform spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A diagonalization property between Hurewicz and Menger.
• \(\gamma\)-sets and other singular sets of real numbers
• Strong \(\gamma\)-sets and other singular spaces
• Some properties of C(X). I
• The combinatorics of Borel covers
• A nonhereditary Borel-cover \(\gamma\)-set
• Combinatorics of open covers. I: Ramsey theory
• A topological interpretation of \({\mathfrak t}\)
• Products of special sets of real numbers
• The combinatorics of open covers. II
• Universally meager sets
• On the length of Borel hierarchies
• Combinatorial Cardinal Characteristics of the Continuum
• On some properties of Hurewicz, Menger, and Rothberger
• Every Lusin set is undetermined in the point-open game
• The algebraic sum of sets of real numbers with strong measure zero sets
• Additivity properties of topological diagonalizations
• Remarks on small sets of reals
• Combinatorics of open covers (VII): Groupability
• Continuous images of sets of reals

This page was built for publication: Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures