TY - JOUR
T1 - A diagonalization property between Hurewicz and Menger
AU - Tsaban, Boaz
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
KW - Continuous images
KW - Hurewicz property
KW - Menger property
KW - Selection principles
UR - http://www.scopus.com/inward/record.url?scp=33746067256&partnerID=8YFLogxK
U2 - 10.14321/realanalexch.27.2.0757
DO - 10.14321/realanalexch.27.2.0757
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AN - SCOPUS:33746067256
SN - 0147-1937
VL - 27
SP - 757
EP - 764
JO - Real Analysis Exchange
JF - Real Analysis Exchange
IS - 2
ER -