Geodesic
On generalized $B^*$-continuity, $B^*$-coverings and $B^*$-separations
Eurasian mathematical journal, Tome 10 (2019) no. 3, pp. 28-39.

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There are various generalizations of continuous functions in topological spaces and $B^*$-continuity is one of them which deals with the Baire property and denseness of the space. We have defined and discussed several properties and interrelations of some further generalizations of $B^*$-continuity, namely, contra $B^*$-continuity, slight $B^*$-continuity and weak $B^*$-continuity. We have also defined certain notions of generalized coverings and separations in terms of $B^*$-sets and studied the effect of generalized $B^*$-continuous functions on spaces having these covering and separation properties. 
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P. Jain; C. Basu; V. Panwar. On generalized $B^*$-continuity, $B^*$-coverings and $B^*$-separations. Eurasian mathematical journal, Tome 10 (2019) no. 3, pp. 28-39. http://geodesic.mathdoc.fr/item/EMJ_2019_10_3_a2/

[1] J. Dontchev, “Contra-continuous functions and strongly $S$-closed spaces”, Int. J. Math. Math. Sci., 19 (1996), 303–310 | MR | Zbl

[2] J. Dontchev, T. Noiri, “Contra-semicontinuous functions”, Math. Pannon., 10 (1999), 159–168 | MR | Zbl

[3] R. L. Ellis, “A non-Archimedean analogue of the Tietze-Urysohn extension theorem”, Nederl. Proc. Akad. Wetensch. Ser. A, 70 (1967), 332–333 | MR | Zbl

[4] D. K. Ganguly, C. Mitra, “$B^*$-continuity and other generalized continuity”, Rev. Acad. Canar. Cienc., XII (2000), 9–17 | MR | Zbl

[5] D. K. Ganguly, C. Mitra, “Some remarks on $B^*$-continuous functions”, Analele Stiintifice Ale universitatii “Al.I.Cuza”, XLVI, no. I, IASI, 2000, 331–336 | MR | Zbl

[6] D. K. Ganguly, C. Mitra, “On some weaker forms of $B^*$-continuity for multifunctions”, Soochow J. Math., 30 (2006), 59–69 | MR

[7] S. Jafari, T. Noiri, “On contra-precontinuous functions”, Bull. Malays. Math. Sci. Soc., 25:2 (2002), 115–128 | MR | Zbl

[8] R. C. Jain, The role of regularly open sets in general topology, Ph. D. thesis, Meerut University, Meerut, 1980

[9] S. Kempisty, “Sur les functions quasi-continues”, Fund. Math., 19 (1932), 184–197

[10] K. Kuratowski, Topology, v. I, Academic Press, New York, 1966 | MR | Zbl

[11] N. Levine, “A decomposition of continuity in topological spaces”, Amer. Math. Monthly, 68 (1961), 44–46 | MR | Zbl

[12] N. Levine, “Semi-open sets and semi-continuity in topological spaces”, Amer. Math. Monthly, 70 (1963), 36–41 | MR | Zbl

[13] M. Matejdes, “Sur les selecteurs des multifonctions”, Math. Slovaca, 37 (1987), 111–124 | MR | Zbl

[14] M. Matejdes, “Continuity of multifunctions”, Real Anal. Exch., 19 (1993), 394–413 | MR

[15] M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mohmoud, “$\beta$-open sets, $\beta$-continuous mapping”, Bull. Fac. Sci. Assiut Univ. A, 12 (1983), 77–90 | MR | Zbl

[16] T. Noiri, “Properties of some weak forms of continuity”, Int. J. Math. Math. Sci., 10 (1987), 97–111 | MR | Zbl

[17] T. Noiri, G. I. Chae, “A note on slightly semi-continuous functions”, Bull. Cal. Math. Soc., 92 (2000), 87–92 | MR | Zbl

[18] T. M. Nour, “Slightly semi continuity”, Bull. Cal. Math. Soc., 87 (1995), 187–190 | MR | Zbl

[19] V. Popa, C. Stan, “On a decomposition of quasi-continuity in topological spaces”, Stud. Cerc. Math., 25 (1973), 41–43 | MR | Zbl

[20] R. Staum, “The algebra of bounded continuous functions into a non-Archimedean field”, Pacific J. Math., 50 (1974), 169–185 | MR | Zbl

[21] A. Vadivel, R. Ramesh, S. Kumar, “Contra $\beta^*$-continuous and almost contra $\beta^*$-continuous function”, Sahand Communications Math. Anal., 8 (2017), 55–71 | Zbl