Notions of β-closure compatible topology with an ideal
Resumen
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.
Descargas
Citas
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.
Derechos de autor 2023 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
