TY - JOUR
T1 - A tall space with a small bottom
AU - Juhász, István
AU - Shelah, Saharon
AU - Soukup, Lajos
AU - Szentmiklóssy, Zoltán
PY - 2003/6
Y1 - 2003/6
N2 - We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if κ<κ = κ, then there is such a space of height κ+ with only κ many isolated points. This implies that there is a locally compact scattered space of height ω2 with ω1 isolated points in ZFC, solving an old problem of the first author.
AB - We introduce a general method of constructing locally compact scattered spaces from certain families of sets and then, with the help of this method, we prove that if κ<κ = κ, then there is such a space of height κ+ with only κ many isolated points. This implies that there is a locally compact scattered space of height ω2 with ω1 isolated points in ZFC, solving an old problem of the first author.
KW - Locally compact scattered space
KW - Superatomic Boolean algebra
UR - http://www.scopus.com/inward/record.url?scp=0037725104&partnerID=8YFLogxK
U2 - 10.1090/s0002-9939-03-06662-0
DO - 10.1090/s0002-9939-03-06662-0
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AN - SCOPUS:0037725104
SN - 0002-9939
VL - 131
SP - 1907
EP - 1916
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 6
ER -