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CARDINAL FUNCTIONS IN TOPOLOGY by I JUHASZ
INTERRELATIONS BETWEEN CARDINAL FUNCTIONS
A1 REGRESSIVE FUNCTIONS
7 other sections not shown
_ exp appendix h arbitrary Assume caliber cardinal function choose cocompact compact space compact Tg space completely regular space completes the proof contradiction Corollary countable defining set definition denote dense subset discrete subspace disjoint family elementary open set ERDOS exists finite free sequence free subset HAJNAL hence holds implies inaccessible cardinal increasing sequence infinite initial segment ir-basis lemma Let us put lexicographic order Martin's axiom Math maximal measurable cardinal non-empty obviously open subsets order topology order type ordered set ordinal pairwise disjoint Proof Let prove quasidisjoint subfamily r-partition Ramsey's theorem regular cardinal Remark right-separated satisfying set mapping set theory singular strong limit subfamily of OC successor successor cardinal Suppose Suslin property theorem topological spaces transfinite induction trivial weakly compact well-ordered