Previous |  Up |  Next

Article

Keywords:
$\mathcal{I}$-regular; codense ideal; $\mathcal{I}$-compact; $\mathcal{I}$-paracompact
Summary:
A new class of spaces which contains the class of all normal spaces is defined and its characterization and properties are discussed.
References:
[1] Hamlett, T. R., Jancović, D.: Compactness with respect to an ideal. Boll. Un. Mat. Ital. B (7) 4 (1990), 849–861. MR 1086708
[2] Hamlett, T. R., Jancović, D.: On weaker forms of paracompactness, countable compactness and Lindelofness. Ann. New York Acad. Sci. 728 (1994), 41–49. DOI 10.1111/j.1749-6632.1994.tb44132.x | MR 1467761
[3] Jancović, D., Hamlett, T. R.: New Topologies from old via ideals. Amer. Math. Monthly 97 (4) (1990), 295 – 310. DOI 10.2307/2324512 | MR 1048441
[4] Kuratowski, K.: Topology, Vol. I. Academic Press, New York, 1966. MR 0217751 | Zbl 0158.40901
[5] Newcomb, R. L.: Topologies which are compact modulo an ideal. Ph.D. thesis, University of Cal. at Santa Barbara, 1967.
[6] Renukadevi, V., Sivaraj, D., Tamizh Chelvam, T.: Codense and Completely codense ideals. Acta Math. Hungar. 108 (3) (2005), 197–205. MR 2162560
[7] Steen, L. A., Seebach, J. A.: Counterexamples in Topology. Springer-Verlag, New York, 1978. MR 0507446 | Zbl 0386.54001
[8] Vaidyanathaswamy, R.: The localization theory in set topology. Proc. Indian Acad. Sci. Math. Sci. 20 (1945), 51–61. MR 0010961
[9] Vaidyanathaswamy, R.: Set Topology. Chelsea Publishing Company, 1946. MR 0115151
[10] Zahid, M. I.: Para-H-closed spaces, locally para-H-closed spaces and their minimal topologies. Ph.D. thesis, Univ. of Pittsburgh, 1981.
Partner of
EuDML logo