Real Analysis Exchange

A Diagonalization Property between Hurewicz and Menger

Boaz Tsaban

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Abstract

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

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

Dates
First available in Project Euclid: 2 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.rae/1212412872

Mathematical Reviews number (MathSciNet)
MR1923165

Zentralblatt MATH identifier
1044.26001

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

Keywords
Menger property Hurewicz property selection principles continuous images

Citation

Tsaban, Boaz. A Diagonalization Property between Hurewicz and Menger. Real Anal. Exchange 27 (2001), no. 2, 757--764. https://projecteuclid.org/euclid.rae/1212412872


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References

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