The combinatorics of Borel covers

Marion Scheepers, Boaz Tsaban

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Abstract

In this paper we extend previous studies of selection principles for families of open covers of sets of real numbers to also include families of countable Borel covers. The main results of the paper could be summarized as follows: (1)Some of the classes which were different for open covers are equal for Borel covers-Section 1. (2)Some Borel classes coincide with classes that have been studied under a different guise by other authors-Section 4.

Original languageEnglish
Pages (from-to)357-382
Number of pages26
JournalTopology and its Applications
Volume121
Issue number3
DOIs
StatePublished - 30 Jun 2002

Bibliographical note

Funding Information:
*Corresponding author. Supported by NSF grant DMS 9971282. E-mail addresses: mslbis@iousa.net (M. Scheepers), tsaban@macs.biu.ac.il (B. Tsaban). URL address: http://www.cs.biu.ac.il/~tsaban (B. Tsaban).

Keywords

  • Borel covers
  • Gerlits-Nagy
  • Lusin set
  • Property γ-sets
  • Rothberger property C″
  • Selection principles
  • Sierpiński set
  • γ-cover
  • ω-cover

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