Some form of open sets and continuity in ideal bitopological spaces

• Autorzy: Noiri Takashi , Popa Valeriu

Identyfikatory

DOI

10.21008/j.0044-4413.2021.0005

• Języki publikacji: EN

Abstrakty

EN

We introduce the notion of (i, j)-mI-open sets as a unified form of (i, j)-α-I-open sets [4], (i, j)-semi-I-open sets [3], (i, j)-pre-I-open sets [1], (i, j)-bI-open sets [17] and (i, j)-β-I-open sets [2]. We show that properties of (i, j)-mI-open sets follow from the properties of minimal open sets in [14]. We introduce and investigate an (i, j)-mI-continuous function from an ideal bitopological space (X, τ1, τ2, I) to a bitopological space (Y, σ1, σ2).

Słowa kluczowe

EN

minimal structure; m-continuous; ideal bitopological space; (i,j)mIO(X)-structure; (i,j)mI-continuous

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2021
• Tom: nr 65
• Strony: 57--66
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Noiri Takashi

• 2949-1 Shiokita-cho, Hinagu, Yatsushiro-shi, Kumamoto-ken, 869-5142 JAPAN

autor

Popa Valeriu

• Department of Mathematics, Univ. Vasile Alecsandri of Bacǎu, 600 115 Bacǎu, RUMANIA

Bibliografia

• [1] Caldas M., Jafari S., Rajesh N., Preopen sets in ideal bitopological spaces, Bol. Soc. Paran. Mat., 29(2)(2011), 61-68.
• [2] Caldas M., Jafari S., Rajesh N., Some fundamental properties of β-open sets in ideal bitopological spaces, Eur. J. Pure Appl. Math., 6(2)(2013), 247-255.
• [3] Caldas M., Jafari S., Rajesh N., Semi-open sets in ideal bitopological spaces, An. Univ. Sci. Budapest., (to appear).
• [4] El-Maghrabi A.I., Caldas M, Jafari S., Latif R.M., Nasef A., Rajesh N, Shanthi S., Properties of ideal bitopological α-open sets, Sci. Stud. Res. Ser. Math. Inform., 27(2)(2017), 15-36.
• [5] Janković D., Hamlett T.R., New topologies from old via ideals, Amer. Math. Monthly, 97(1990), 295-310.
• [6] Kelly J.K., Bitopological spaces, Proc. London Math. Soc., 13(3)(1963), 71-89.
• [7] Kuratowski K., Topology, Vol. I, Acadmic Press, New York, 1966.
• [8] Maki H., Rao C.K., Gani A. Nagoor, On generalizing semi-open and preopen sets, Pure Appl. Math. Sci., 49(1999), 17-29.
• [9] Newcomb R.L., Topologies which are compact modulo an ideal, Ph. D. Thesis, University of California, USA (1967).
• [10] Noiri T., Popa V., A new viewpoint in the study of irresoluteness forms in bitopological spaces, J. Math. Anal. Approx. Theory, 1(1)(2006), 1-9.
• [11] T., Noiri T., Popa V., A new viewpoint in the study of continuity forms in bitopological spaces, Kochi J. Math., 2(2007), 95-106.
• [12] Pervin W.J., Connectedness in bitopological spaces, Indag. Math., 29(1967), 369-372.
• [13] Popa V., Noiri T., On M-continuous functions, Anal. Univ. ”Dunǎrea de Jos” Galąti, Ser. Mat. Fiz. Mec. Teor., Fasc. II, 18(23)(2000), 31-41.
• [14] Popa V., Noiri T., On the definitions of some generalized forms of continuity under minimal conditions, Mem. Fac. Sci. Kochi Univ. Ser. Math., 22(2001), 9-18.
• [15] Popa V., Noiri T., On the points of continuity and discontinuity, Bul. U. P. G. Ploiesti, Ser. Mat. Inf. Fiz., 53(1)(2001), 95–100.
• [16] Popa V., Noiri T., A unified theory of weak continuity for functions, Rend Circ. Mat. Palermo (2)(51)(2002), 439-464.
• [17] Sarma D.J., bI-open sets in ideal bitopological spaces, Int. J. Pure Appl. Math., 105(1)(2015), 7-18.
• [18] Vaidyanathaswani R., The localization theory in set-topology, Proc. Indian Acad. Sci., 20(1945), 51-62.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).