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

Maddalena Bonanzinga 1 , Maria Cuzzupé 1 ,  and Bruno Pansera 1
  • 1 Dipartimento di Matematica e Informatica, Università di Messina, Viale F. Stagno d’Acontres 31, 98166, Messina, Italy

Abstract

Two variations of Arhangelskii’s inequality $$\left| X \right| \leqslant 2^{\chi (X) - L(X)}$$ 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.

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