Two variations of Arhangelskii’s inequality 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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0339-0,
author = {Maddalena Bonanzinga and Maria Cuzzup\'e and Bruno Pansera},
title = {On the cardinality of n-Urysohn and n-Hausdorff spaces},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {330-336},
zbl = {1287.54005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0339-0}
}
Maddalena Bonanzinga; Maria Cuzzupé; Bruno Pansera. On the cardinality of n-Urysohn and n-Hausdorff spaces. Open Mathematics, Tome 12 (2014) pp. 330-336. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0339-0/
[1] Arhangel’skii A.V., The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR, 1969, 187, 967–970 (in Russian)
[2] Arhangel’skii A.V., A generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carolin., 1995, 36(2), 303–325
[3] Bella A., Cammaroto F., On the cardinality of Urysohn spaces, Canad. Math. Bull., 1988, 31(2), 153–158 http://dx.doi.org/10.4153/CMB-1988-023-4 | Zbl 0646.54005
[4] Bonanzinga M., On the Hausdorff number of a topological space, Houston J. Math., 2013, 39(3), 1013–1030 | Zbl 1290.54003
[5] Bonanzinga M., Cammaroto F., Matveev M.V., On a weaker form of countable compactness, Quaest. Math., 2007, 30(4), 407–415 http://dx.doi.org/10.2989/16073600709486209 | Zbl 1144.54012
[6] Bonanzinga M., Cammaroto F., Matveev M., On the Urysohn number of a topological space, Quaest. Math., 2011, 34(4), 441–446 http://dx.doi.org/10.2989/16073606.2011.640456 | Zbl 1274.54016
[7] Bonanzinga M., Cammaroto F., Matveev M., Pansera B., On weaker forms of separability, Quaest. Math., 2008, 31(4), 387–395 http://dx.doi.org/10.2989/QM.2008.31.4.7.611 | Zbl 1155.54328
[8] Bonanzinga M., Pansera B., On the Urysohn number of a topological space II, Quaest. Math. (in press) | Zbl 1164.54352
[9] Carlson N., The weak Lindelöf degree and homogeneity (manuscript) | Zbl 1263.54005
[10] Carlson N.A., Porter J.R., Ridderbos G.J., On cardinality bounds for homogeneous spaces and G κ-modification of a space, Topology Appl., 2012, 159(13), 2932–2941 http://dx.doi.org/10.1016/j.topol.2012.05.004 | Zbl 1267.54006
[11] Engelking R., General Topology, 2nd ed., Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989
[12] Gryzlov A.A., Stavrova D.N., Topological spaces with a selected subset - cardinal invariants and inequalities, C. R. Acad. Bulgare Sci., 1993, 46(7), 17–19 | Zbl 0809.54002
[13] Hodel R.E., Cardinal functions I, In: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 1–61
[14] Hodel R.E., Combinatorial set theory and cardinal functions inequalities, Proc. Amer. Math. Soc., 1991, 111(2), 567–575 http://dx.doi.org/10.1090/S0002-9939-1991-1039531-7 | Zbl 0713.54007
[15] Hodel R.E., Arhangel’skiĭ’s solution to Alexandroff’s problem: A survey, Topology Appl., 2006, 153(13), 2199–2217 http://dx.doi.org/10.1016/j.topol.2005.04.011 | Zbl 1099.54001
[16] Ramírez-Páramo A., Tapia-Bonilla N.T., A generalization of a generic theorem in the theory of cardinal invariants of topological spaces, Comment. Math. Univ. Carolin., 2007, 48(1), 177–187 | Zbl 1199.54034
[17] Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333–343 | Zbl 1027.54006
[18] Veličko N.V., H-closed topological spaces, Mat. Sb. (N.S.), 1966, 70(112)(1), 98–112 (in Russian)
[19] Willard S., Dissanayeke U.N.B., The almost Lindelöf degree, Canad. Math. Bull., 1984, 27(4), 452–455 http://dx.doi.org/10.4153/CMB-1984-070-2 | Zbl 0551.54003