Atlas: On weakly semi-I-open sets and another decomposition of continuity via ideals by Esref Hatir

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International Conference on Applicable General Topology
August 12-18, 2001
Hacettepe University
Ankara, Turkey

Organizers
L. M. Brown (Ankara), G. Brümmer (Cape Town), M. Diker (Ankara), M. Henriksen (Claremont), R. D. Kopperman (New York), G. M. Reed (Oxford), I. L. Reilly (Auckland), S. Salbany (Pretoria), D. Spreen (Siegen)

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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