Application of ic—open Sets in Topologies Via Ideals

AL -jaheishi, Rana Ibraheem; AL- Siraj, Amir

doi:10.33899/csmj.2024.146288.1104

	Application of ic—open Sets in Topologies Via Ideals
AL-Rafidain Journal of Computer Sciences and Mathematics
Volume 18, Issue 1, June 2024, Pages 92-95 PDF (403.04 K)
Document Type: Review Paper
DOI: 10.33899/csmj.2024.146288.1104
Authors
Rana Ibraheem AL -jaheishi^* ; Amir AL- siraj
Department of Mathematics, College of Education for Pure Sciences, University of Mosul, Iraq
Abstract
In this paper, new kinds of open sets inside ideal topological spaces are introduced; they are called ic - I - open,icc - I -open,weakly ic - I - open and weakly icc - I - open. Some properties and relations between these new classes are studied with examples. The concept of continuity in ideal topological spaces is also presented for these new classes. Theorems that provide an equivalence relation between these new classes are proved. Also, for ideal topological spaces (Ɲ, Ʈ, I) we show that all open sets are ic -I- open, icc - I - open, weakly ic - I - open, weakly icc - I - open . Finally, Assume Z ⊂ Ɲ of ideal Topological spaces (Ɲ,Ʈ,l ). Then 1) if Z is semi - I - open, then Z^c is ic – I - open. 2) if Z is open and ic - I - closed, then Z is semi - I - open.
Keywords
Ideal topological Space; ic-I-open; icc-I-open

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