Cardinal functions for topological spaces in which a subset is selected in a certain way are defined and studied. Most of the main cardinal inequalities are generalized for such spaces.
@article{118692,
author = {Anatoly A. Gryzlov and Dimitrina N. Stavrova},
title = {Topological spaces with a selected subset-cardinal invariants and inequalities},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {35},
year = {1994},
pages = {525-531},
zbl = {0869.54007},
mrnumber = {1307279},
language = {en},
url = {http://dml.mathdoc.fr/item/118692}
}
Gryzlov, Anatoly A.; Stavrova, Dimitrina N. Topological spaces with a selected subset-cardinal invariants and inequalities. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 525-531. http://gdmltest.u-ga.fr/item/118692/
On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), 951-955. (1969)
A theorem about cardinality, Uspehi Matem. Nauk 34 (1979), 177-178. (1979) | MR 0548421
The position of subspaces in a topological space: relative compactness, Lindelöfness and axioms of separation, Vestnik Moskovskogo Universiteta, ser I., vol. 6, 1989, 67-69.
Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79 (1978), 37-45. (1978) | MR 0526665
General Topology, Warszawa, 1976. | Zbl 0684.54001
Discrete Subspaces of Topological Spaces I & II, Pc. Koninkl. Nederl. Akad. Wet., Ser. A, 70 (1967), 343-356; 72 (1969), 18-30. | MR 0264585
Cardinal Functions in Topology - Ten Years Later, Math. Centre Tracts 123, Amsterdam, 1980. | MR 0576927 | Zbl 0479.54001
Two cardinal functions of topological spaces and improvements of some famous cardinal inequalities, Acta Math. Sinica 29 (1986), 494-497. (1986) | MR 0867698
A note on Archangel'skii's inequality, J. Math. Soc. Japan 39 (1987), 363-365. (1987) | MR 0900974
A New Inequality for the Cardinality of topological Spaces, Proc. of the XX-th Conf. of the UBM, 1991.