Mizokami and Lin's conjecture on σ-CF~* pseudo-bases

摘要

Mizokami and Lin conjectured in (T. Mizokami. S. Lin, On spaces with a σ-CF~* pseudo-base. Math. Jpn. 46 (1997) 377-384]: Every space X with a σ-CF~* pseudo-base satisfies that either X is an N_0 -space or each compact subset of X is finite. In this paper we show this conjecture is true. Also we answer some other questions in the book "Open Problems in Topology, II".