The combinatorics of Borel covers

Marion Scheepers; Boaz Tsaban

doi:10.1016/S0166-8641(01)00078-5

The combinatorics of Borel covers

Marion Scheepers
, Boaz Tsaban

Mathematics Department

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

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 language	English
Pages (from-to)	357-382
Number of pages	26
Journal	Topology and its Applications
Volume	121
Issue number	3
DOIs	https://doi.org/10.1016/S0166-8641(01)00078-5
State	Published - 30 Jun 2002

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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10.1016/S0166-8641(01)00078-5

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AB - 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.

KW - Borel covers

KW - Gerlits-Nagy

KW - Lusin set

KW - Property γ-sets

KW - Rothberger property C″

KW - Selection principles

KW - Sierpiński set

KW - γ-cover

KW - ω-cover

UR - https://www.scopus.com/pages/publications/0038351767

U2 - 10.1016/S0166-8641(01)00078-5

DO - 10.1016/S0166-8641(01)00078-5

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AN - SCOPUS:0038351767

SN - 0166-8641

VL - 121

SP - 357

EP - 382

JO - Topology and its Applications

JF - Topology and its Applications

IS - 3

ER -

The combinatorics of Borel covers

Abstract

Keywords

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