The relativization of Gryzlov's theorem about the size of compact $T_1$-spaces with countable pseudocharacter is false.
@article{118839, author = {Winfried Just}, title = {The sizes of relatively compact $T\_1$-spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {37}, year = {1996}, pages = {379-380}, zbl = {0847.54024}, mrnumber = {1399009}, language = {en}, url = {http://dml.mathdoc.fr/item/118839} }
Just, Winfried. The sizes of relatively compact $T_1$-spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 379-380. http://gdmltest.u-ga.fr/item/118839/
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