Some new directions in infinite-combinatorial topology

Abstract

We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are stated. Some results which do not appear elsewhere are also included, with proofs.

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References in corpus (12)

• The combinatorics of Borel covers
• Hereditary topological diagonalizations and the Menger-Hurewicz Conjectures
• o-bounded groups and other topological groups with strong combinatorial properties
• Strong gamma-sets and other singular spaces
• Additivity properties of topological diagonalizations
• Selection principles in mathematics: A milestone of open problems
• The combinatorics of splittability
• Critical cardinalities and additivity properties of combinatorial notions of smallness
• Additivity numbers of covering properties
• The minimal cardinality where the Reznichenko property fails
• The combinatorics of tau-covers
• SPM Bulletin 1

Cited by in corpus (16)

• Selective covering properties of product spaces
• Products of Menger spaces in the Miller model
• On the Kocinac alpha_i properties
• The combinatorics of the Baer-Specker group
• Pointwise convergence of partial functions: The Gerlits-Nagy Problem
• Squares of Menger-bounded groups
• Superfilters, Ramsey theory, and van der Waerden's Theorem
• The combinatorics of tau-covers
• Notes on linearly H-closed spaces and od-selection principles
• Menger's covering property and groupwise density
• Can a Borel group be generated by a Hurewicz subspace?
• A new selection principle
• Omission of Intervals: Deducing covering properties of subsets of the real line from their combinatorial structure
• Classification of selectors for sequences of dense sets of Cp(X)
• Further observations on bornological covering properties and selection principles
• The functional characteristics of the Rothberger and Menger properties