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Characterizations of \(\theta\)-closed sets using separation axioms in ideal topological spaces. (English) Zbl 1383.54004

Summary: We will give various characterizations of \(\theta\)-closed sets with respect to an ideal using separation axioms. Also give its relationship with other type of closed sets defined in literature.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D30 Compactness
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References:

[1] A. Al-Omari and Takashi Noiri, Onθ(I,J)- continuous functions,Rend. Istit. Mat. Univ. Trieste, 44(2012), 399-411. · Zbl 1263.54029
[2] ‘A. Cs‘asz‘ar, General Topology , A. Hilger Ltd., Bristol, 1978.
[3] R. F. Dickman Jr. and J.R. Porter,θ -perfect and θ-absolutely closed functions, Illinois J. Math, 21(1977), 42-60. · Zbl 0351.54010
[4] N. Goyal and N. S. Noorie, I-convergence andτ∗-closedness of I-compact sets, Journal of Advanced studies in Topology, 8(2017),78-84. · Zbl 1378.54024
[5] D. Jankovi´c and T.R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly, 97(1990), no. 4, 295-310. · Zbl 0723.54005
[6] D. Jankovi´c, On some separation axioms andθ-closure, Mat. Vesnik, 32(4) (1980), 439-449. · Zbl 0528.54016
[7] K. Kuratowski, Topology, volume I, Academic Press, New York, 1966. · Zbl 0158.40802
[8] D. Sivaraj and V. Renukadevi, Some Seperation Axioms via ideals, Boll. U. M. I., 3(2007), 3-B.
[9] L. A. Steen and J. A. Seebach Jr., Counterexamples in topology, Holt, Rinehart and Winston, Inc., 1970. · Zbl 0211.54401
[10] R. Vaidyanathaswamy, The localisation Theory in Set Topology, Proc. Indian Acad. Sci., 20(1945), 51-61. · Zbl 0061.39308
[11] , Set Topology, Chelsea Publishing Company, New York, 1946.
[12] N.V. Veliˇcko, H-closed topological spaces, Mat. Sb., 79(112) (1966), 98-112. · Zbl 0178.56503
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