TY - JOUR
T1 - Hereditary topological diagonalizations and the Menger-Hurewicz conjectures
AU - Bartoszýnski, Tomek
AU - Tsaban, Boaz
PY - 2006/2
Y1 - 2006/2
N2 - We consider the question of which of the major classes defined by topological diagonalizations of open or Borel covers is hereditary. Many of the classes in the open case are not hereditary already in ZFC, and none of them are provably hereditary. This is in contrast with the Borel case, where some of the classes are provably hereditary. Two of the examples are counter-examples of sizes 8 and b, respectively, to the Menger and Hurewicz Conjectures, and one of them answers a question of Steprans on perfectly meager sets.
AB - We consider the question of which of the major classes defined by topological diagonalizations of open or Borel covers is hereditary. Many of the classes in the open case are not hereditary already in ZFC, and none of them are provably hereditary. This is in contrast with the Borel case, where some of the classes are provably hereditary. Two of the examples are counter-examples of sizes 8 and b, respectively, to the Menger and Hurewicz Conjectures, and one of them answers a question of Steprans on perfectly meager sets.
KW - Hurewicz property
KW - Menger property
KW - Selection principles
KW - Strong γ-set
UR - http://www.scopus.com/inward/record.url?scp=33644556522&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-05-07997-9
DO - 10.1090/S0002-9939-05-07997-9
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AN - SCOPUS:33644556522
SN - 0002-9939
VL - 134
SP - 605
EP - 615
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 2
ER -