TY - JOUR
T1 - Combinatorial aspects of selective star covering properties in Ψ-spaces
AU - Tsaban, Boaz
N1 - Publisher Copyright:
© 2015 Elsevier B.V.
PY - 2015/9/1
Y1 - 2015/9/1
N2 - Which Isbell-Mrówka spaces (Ψ-spaces) satisfy the star version of Menger's and Hurewicz's covering properties? Following Bonanzinga and Matveev, this question is considered here from a combinatorial point of view. An example of a Ψ-space that is (strongly) star-Menger but not star-Hurewicz is obtained. The PCF-theory function κcof([κ]ℵ0) is a key tool. Using the method of forcing, a complete answer to a question of Bonanzinga and Matveev is provided.The results also apply to the mentioned covering properties in the realm of Pixley-Roy spaces, to the extent of spaces with these properties, and to the character of free abelian topological groups over hemicompact k spaces.
AB - Which Isbell-Mrówka spaces (Ψ-spaces) satisfy the star version of Menger's and Hurewicz's covering properties? Following Bonanzinga and Matveev, this question is considered here from a combinatorial point of view. An example of a Ψ-space that is (strongly) star-Menger but not star-Hurewicz is obtained. The PCF-theory function κcof([κ]ℵ0) is a key tool. Using the method of forcing, a complete answer to a question of Bonanzinga and Matveev is provided.The results also apply to the mentioned covering properties in the realm of Pixley-Roy spaces, to the extent of spaces with these properties, and to the character of free abelian topological groups over hemicompact k spaces.
KW - Isbell-Mrówka space
KW - Star-Hurewicz
KW - Star-Menger
KW - Ψ-space
UR - http://www.scopus.com/inward/record.url?scp=84939564305&partnerID=8YFLogxK
U2 - 10.1016/j.topol.2015.05.082
DO - 10.1016/j.topol.2015.05.082
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AN - SCOPUS:84939564305
SN - 0166-8641
VL - 192
SP - 198
EP - 207
JO - Topology and its Applications
JF - Topology and its Applications
ER -