On weakly semi-I-open sets and another decomposition of continuity via ideals
by
Esref Hatir
Selcuk University, Konya,Turkey
Coauthors: Saeid Jafari (Department of Mathematics and Physics, Roskilde University, Denmark)

Topological ideals have played an important role in topology for several years. It was the works of Newcomb [7], Rancin [8], Samuels [9] and Hamlet and Jankovic [1, 2, 3, 4, 6] which motivated the research in applying topological ideals to generalize the most basic properties in general topology. Quite recently, Noiri and I [5] introduced and investigated the new notion of semi-I-open sets with respect to topological ideals.

It is the aim of this talk to offer and study a new class of sets called weakly semi-I-open sets by utilizing topological ideals. We also introduce the class of weakly semi-I-continuity by which we obtain a new decomposition of continuity.

References

[1] T. R. Hamlett and D. S. Jankovic, Compactness with respect to an ideal, Boll. Un. Mat. Ital. (7), 4-B, (1990), 849-861.

[2] T. R. Hamlett and D. S. Jankovic, Ideals in topological spaces and the set operator, Boll. Un. Mat. Ital. 7, (1990), 863-874.

[3] T. R. Hamlett and D. S. Jankovic, Ideals in General Topology and Applications (Middletown, CT, 1988), 115-125; SE: Lecture Notes in Pure and Appl. Math. 123, (1990), Dekker, New York.

[4] T. R. Hamlett and D. S. Jankovic, Compatible extensions of ideals, Boll. Un. Mat. Ital. 7, (1992), 453-465.

[5] E. Hatir and T. Noiri, On decomposition of continuity via idealization (submitted).

[6] D. S. Jankovic and T. R. Hamlett , New topologies from old via ideals, Amer. Math. Monthly 97, (1990), 295-310.

[7] R. L. Newcomb, Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. Cal. at Santa Barbara, 1967.

[8] D. V. Rancin, Compactness modulo an ideal, Soviet Math. Dokl. 13, (1972), 193-197.

[9] P. Samuels, A topology from a given topology and ideal, J. London Math. Soc. (2)(10), (1975), 409-416.

Date received: June 20, 2001