On Weakly Semi-I-Open Sets and Another Decomposition of Continuity via Ideals
DOI:
https://doi.org/10.5644/SJM.02.1.11Keywords:
Weakly semi-I-open set, weakly semi-I-continuousAbstract
In this paper, we introduce the notions of weakly semi-I-open set and weakly semi-I-continuous functions to obtain a decomposition of continuity. We also investigated the fundamental properties of such functions.
1991 Mathematics Subject Classification. Primary: 54C10, 54A05; Secondary: 54D25, 54D30
Downloads
References
M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12 (1983), 77–90.
M. E. Abd El-monsef, E. F. Lashien and A. A. Nasef, On I-open sets and I-continuous functions, Kyungpook Math., 32 (1992), 21–30.
J. Dontchev, On pre-I-open sets and a decomposition of I-continuity, Banyan Math. J., 2 (1996).
T. R. Hamlett and D. S. Jankovic, Compactness with respect to an ideal, Boll. Un. Mat. Ital., (7), 4-B, (1990), 849–861.
T. R. Hamlett and D. S. Jankovic, Ideals in topological spaces and the set operator, Boll. Un. Mat. Ital., 7 (1990), 863–874.
T. R. Hamlett and D. S. Jankovic, Ideals in General Topology and Applications (Middletown, CT, 1988), 115–125, Lecture Notes in Pure and Appl. Math., 123, Dekker, New York,(1990).
T. R. Hamlett and D. S. Jankovic, Compatible extensions of ideals, Boll. Un. Mat. Ital., 7 (1992), 453–465.
E. Hatir and T. Noiri, On decomposition of continuity via idealization, Acta Math. Hungar., 96 (4) (2002), 341–349.
E. Hayashi, Topologies defined by local properties, Math. Ann., 156 (1964), 205–215.
D. S. Jankovic and T. R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly, 97 (1990), 295–310.
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36–41.
A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47–53.
R. L. Newcomb, Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. Cal. at Santa Barbara, 1967.
D. V. Rancin, Compactness modulo an ideal, Soviet Math. Dokl., 13 (1972), 193–197.
P. Samuels, A topology from a given topology and ideal, J. London Math. Soc., (2) (10) (1975), 409–416.
