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relatively compact; relatively Lindelöf; $T_1$-space; measurable cardinal
The relativization of Gryzlov's theorem about the size of compact $T_1$-spaces with countable pseudocharacter is false.
[A] Arhangel'skii A.V.: A generic theorem in the theory of cardinal invariants of topological spaces. Comment. Math. Univ. Carolinae 36.2 (1995), 303-325. MR 1357532
[AC] Antonovskii M.Y., Chudnovskii D.V.: Some questions of general topology and Tikhonov semifields II. Russian Math. Surveys 31.3 (1976), 69-128.
[G] Gryzlov A.A.: Two theorems on the cardinality of topological spaces. Soviet Math. Dokl. 21.2 (1980), 506-509. MR 0568530 | Zbl 0449.54005
[R] Ranchin D.V.: On compactness modulo an ideal. Soviet Math. Dokl. 13.1 (1972), 193-197.
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