Characterizations of Rarely $g$-Continuous Multifunctions
DOI:
https://doi.org/10.5644/SJM.01.1.11Keywords:
Rare set, $g$-open, rarely $g$-continuous multifunctionsAbstract
In 1979, Popa [15] introduced the notion of rare continuity. Quite recently, the authors [3] introduced and investigated a new class of functions called rarely $g$-continuous functions as a generalization of both rare continuity and weak $g$-continuity [5]. In this paper, we introduce and study the new notion of upper (lower) rarely $g$-continuous multifunctions as a generalization of upper (lower) weakly continuous multifunctions [13].
2000 Mathematics Subject Classification. 54C60, 54C08; Secondary: 54D05
Downloads
References
K. Balachandran, P. Sundaran and H. Mak, On generalized continuous maps in topological spaces, Mem. Fac. Sci. Kochi Univ. (Ser. A Math.), 12 (1991), 5–13.
M. Caldas, On g–closed sets and g–continuous mappings, Kyungpook Math. J., 33 (1993), 205–209.
M. Caldas and S. Jafari, On rarely g–continuous functions, Glas. Mat. Ser. III (to appear).
M. Caldas, S. Jafari and T. Noiri, Characterizations of weakly g–continuous multifunctions (under preparation).
M. Caldas, S. Jafari and T. Noiri, Properties of weakly g–continuous functions (under preparation.
Dunham, T1/2–spaces, Kyungpook Math. J., 17 (1977), 161–169.
Dunham and N. Levine, Further results on generalized closed sets in topology, Kyungpook Math. J., 20 (1980), 164–175.
S. Jafari, A note on rarely continuous functions, Stud. Cercet. Stiint., Ser. Mat., Univ. Bacau, 5 (1995), 29–34.
S. Jafari, On some properties of rarely continuous functions, Stud. Cercet. Stiint., Ser. Mat., Univ. Bacau, 7 (1997), 65–73.
N. Levine, A decomposition of continuity in topological spaces, Amer. Math. Monthly, (60) (1961), 44–46.
N. Levine, Generalized closed sets in topological, Rend. Circ. Mat. Palermo, 19 (2)(1970), 89–96.
P. E. Long and L. L. Herrington, Properties of rarely continuous functions, Glas. Mat. Ser. III 17 (37) (1982), 147–153.
V. Popa, Weakly continuous multifunctions, Boll. Unione Mat. Ital., (5), 15(A) (1978), 379–388.
V. Popa, Some properties of rarely continuous multifunctions, Conf. Nat. Geom. Topologie, Univ. Al. I. Cuza Iasi, (1989), 269–274.
V. Popa, Sur certain decomposition de la continuit´e dans les espaces topologiques, Glas. Mat. Ser. III, 14 (34)(1979), 359–362.
