On the cardinality of n-Urysohn and n-Hausdorff spaces

Two variations of Arhangelskii's inequality (Formula presented.) for Hausdorff X [Arhangel'skii A.V., The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR, 1969, 187, 967-970 (in Russian)] given in [Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333-343] are extended to the classes with finite Urysohn number or finite Hausdorff number. © 2014 Versita Warsaw and Springer-Verlag Wien.