Some Classes in Ideal Topological Spaces

Jadoo, Mohammed Wasfi; Alsaraj, Amir A .Mohammed

doi:10.33899/edusj.2023.137766.1318

	Some Classes in Ideal Topological Spaces
Journal of Education and Science
Article 32, Volume 32, Issue 2, 2023, Pages 128-133 PDF (690.37 K)
Document Type: Review Paper
DOI: 10.33899/edusj.2023.137766.1318
Authors
Mohammed wasfi Jadoo^* ; Amir A .Mohammed Alsaraj
Department of Mathematics, College of Education for Pure Sciences, Mosul University, Mosul, Iraq
Abstract
This study presents new classes of open sets defined in ideal topological space. These classes, namely: i - I -open, weakly i- I-open, ii - I -open, and weakly ii -I -open. Also, we gave new concepts of continuity of a mapping between ideal topological spaces using these classes, such as: i –I- continuity weakly i-I-continuity, ii-continuity, and weakly ii-I-continuity. We got their characteristics with comparisons of these classes and concepts. We prove that all open sets, α – I-open, semi - I - open, ii - I-open, weakly semi - I-open, and weakly ii-I-open, sets are weakly i-I-open for any ideal topological space. Additionally, we show that all α –I-continuous, semi-I-continuous, and ii-I-continuous mappings are i-I-continuous. Finally, for ideal topological space (M,L,I) and D ⊂ M satisfying 〖Int(D)〗^#= Int(D), We show that the following statements are equal.: 1) D is open 2) D is i-I-open and D∩H = Int(D) for some H ∈ L∖ {M,∅} 3) D is semi-I-open. Similarly, We show that the following statements are equal.: 1) D is a closed set, 2) (D∩F) = cl(D) for some F ∈ L^c 3) D is semi-I-closed.
Keywords
.Ideal topological space,,; ,،,؛i-open,,; ,،,؛ii-open

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