Real Analysis Exchange

A Diagonalization Property between Hurewicz and Menger

Boaz Tsaban

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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. We also find some additivity numbers for these classes. This paper can serve as an exposition of this fascinating subject.

Article information

Real Anal. Exchange, Volume 27, Number 2 (2001), 757-764.

First available in Project Euclid: 2 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Menger property Hurewicz property selection principles continuous images


Tsaban, Boaz. A Diagonalization Property between Hurewicz and Menger. Real Anal. Exchange 27 (2001), no. 2, 757--764.

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