The Hurewicz covering property and slaloms in the Baire space

• Autorzy: Boaz Tsaban
• Języki publikacji: EN

Abstrakty

EN

According to a result of Kočinac and Scheepers, the Hurewicz covering property is equivalent to a somewhat simpler selection property: For each sequence of large open covers of the space one can choose finitely many elements from each cover to obtain a groupable cover of the space. We simplify the characterization further by omitting the need to consider sequences of covers: A set of reals X has the Hurewicz property if, and only if, each large open cover of X contains a groupable subcover. This solves in the affirmative a problem of Scheepers. The proof uses a rigorously justified abuse of notation and a "structure" counterpart of a combinatorial characterization, in terms of slaloms, of the minimal cardinality 𝔟 of an unbounded family of functions in the Baire space. In particular, we obtain a new characterization of 𝔟.

Kategorie tematyczne

• 37F20: Combinatorics and topology
• 26A03: Foundations: limits and generalizations, elementary topology of the line
• 03E75: Applications of set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 3
• Strony: 273-280

Daty

wydano

2004

Twórcy

autor

Boaz Tsaban

• Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel

Identyfikatory

DOI

10.4064/fm181-3-5