A diagonalization property between Hurewicz and Menger

Details A diagonalization property between Hurewicz and Menger A diagonalization property between Hurewicz and Menger

2001-06-11

arxiv.org/abs/math/0106085v4

Real Analysis Exchange 27 (2001/2002), 757--763

Mathematics

General Topology

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Scientific paper

In classical works, Hurewicz and Menger introduced two diagonalization properties for sequences of open covers. Hurewicz found a combinatorial characterization of these notions in terms of continuous images. Recently, Scheepers has shown that these notions are particular cases in a large family of diagonalization schemas. One of the members of this family is weaker than the Hurewicz property and stronger than the Menger property, and it was left open whether it can be characterized combinatorially in terms of continuous images. We give a positive answer. This paper can serve as an exposition of this fascinating subject.

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