Notions of β-closure compatible topology with an ideal
Abstract
In this paper, we have defined β-local closure function. Its properties and characterizations are analyzed. The set operator is defined and its properties are discussed. The notions of β-closure compatible topology with an ideal are introduced and investigated. Moreover, dense set and -codense ideal are defined and explored.
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References
Abd EI-Monsef .M. E., Lashien E. F. and Nasef.A.A, Some topological operators via ideals, Kyungpook Mathematical Journal, Vol 32, No. 2, (1992).
Ahmad Al-Omari, Takashi Noiri, Local closure function in ideal topological spaces. Novi Sad J. Math. Vol. 43, No. 2, (2013), 139-149.
Andrijevic. D, Semi-preopen sets, Mat. Vesnik, Vol.38, (1986), 24-32.
Belal Nairat, On Some Properties of B-open sets, International Journal of Applied Engineering Research, Vol.13, No.6, (2018), 3670-3672.
Dlaska. K, Ergun. N and Ganster. M, On the topology generated by semi-regular sets, Indian J. Pure Appl. Math., Vol.25 (1994), no.11, 1163 – 1170.
Dontchev.J, Ganster.M and Rose.D, Ideal resolvability, Topology and its Applications, 93 (1999), 1-16.
Hatir.E, Keskin.A and Noiri.T, On a new decomposition of continuity via idealization, JP Jour. Geometry and Topology, 3 (2003), no.1, 53 – 64,.
Hayashi. E, Topologies defined by local properties, Math. Ann. 156 (1964), 205–215,
Jankovic. D, Hamlett. T.R, New topologies from old via ideals, American. Math. Monthly, 97 (1990), no.4, 295 – 310.
Jessie Theodore and Beulah. V, On gB I-closed sets in the ideal topological spaces, Global Journal of Pure and Applied Mathematics, 13 (2017), no.9, 6155 – 6165.
Kuratowski. K, Topology I, Warszawa, (1933).
Levine. N, Semi-open sets and semi-continuity in topological spaces, American. Math. Monthly, 70 (1963), 36 – 41.
Newcomb. R. L, Topologies which are compact modulo an ideal, Ph.D.dissertation, Univ. of Cal. at Santa Barbara, (1967).
Njastad. O, Remarks on topologies defined by local properties, Avh. Norske Vid. Akad. Oslo, 1 (1966), no.8, 1 – 16.
Vaidyanathaswamy. R, Set Topology, Chelsea Publishing Company, (1960).
Vaidyanathaswamy. R, The localization theory in Set-topology, Proc. Indian Acad. Sci. 20 (1945), 51 – 61.
Velicko. N. V, H -closed topological spaces, American Mathematical Society Translations, 78 (1968), 103 – 118.
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