A diagonalization property between Hurewicz and Menger

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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. This paper can serve as an exposition of this fascinating subject.

Original languageEnglish
Pages (from-to)757-764
Number of pages8
JournalReal Analysis Exchange
Issue number2
StatePublished - 2002


  • Continuous images
  • Hurewicz property
  • Menger property
  • Selection principles


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