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

• Autorzy: Maddalena Bonanzinga , Maria Cuzzupé , Bruno Pansera
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Urysohn number of a space; Hausdorff number of a space; $$cl^\mathcal{H}$$-operator; θ-closure; $$cl_\theta ^\mathcal{H}$$-operator; Relative Lindelöf number; Almost Lindelöf degree of a space

Kategorie tematyczne

• 54D10: Lower separation axioms ( T 0 -- T 3 , etc.)
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 2
• Strony: 330-336

Daty

wydano

2014-02-01

online

2013-11-21

Twórcy

autor

Maddalena Bonanzinga

• Università di Messina

autor

Maria Cuzzupé

• Università di Messina

autor

Bruno Pansera

• Università di Messina

Bibliografia

• [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
• [4] Bonanzinga M., On the Hausdorff number of a topological space, Houston J. Math., 2013, 39(3), 1013–1030
• [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
• [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
• [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
• [8] Bonanzinga M., Pansera B., On the Urysohn number of a topological space II, Quaest. Math. (in press)
• [9] Carlson N., The weak Lindelöf degree and homogeneity (manuscript)
• [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
• [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
• [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
• [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
• [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
• [17] Stavrova D.N., Separation pseudocharacter and the cardinality of topological spaces, Topology Proc., 2000, 25(Summer), 333–343
• [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

Identyfikatory

DOI

10.2478/s11533-013-0339-0