Abstract
References
- [1] A. Al-Omari, Soft topology in ideal topological spaces, Hacet. J. Math. Stat. 48 (5), 1277-1285, 2019.
- [2] A. Al-Omari and T. Noiri, Local closure functions in ideal topological spaces, Novi Sad J. Math. 43 (2), 139-149, 2013.
- [3] A. Al-Omari and T. Noiri, Local function $\Gamma^{*}$ in ideal topological spaces, Sci. Stud. Res. Ser. Math. Inform. 26 (1), 5-16, 2016.
- [4] A. Al-Omari and T. Noiri, On operators in ideal minimal spaces, Mathematica 58 (81), 3-13, 2016.
- [5] J. Dontchev and M. Ganster, On compactness with respect to countable extensions of ideals and the generalized Banach Category Theorem, Acta. Math. Hungar. 88 (1-2), 53-58, 2000.
- [6] J. Dontchev, M. Ganster and D. Rose, Ideal resolvability, Topology Appl. 93 (1), 1-16, 1999.
- [7] E. Hatir, A. Al-Omari and S. Jafari, $\delta$-Local functions and its properties in ideal topological spaces, Fasc. Math. 53, 53-64, 2014.
- [8] E. Hewitt, A problem of set-theoretic topology, Duke Math. J. 10, 309-333, 1943.
- [9] D. Jankovic and T.R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly 97, 295-310, 1990.
- [10] D. Jankovic and Ch. Konstadilaki, On covering properties by regular closed sets, Math. Pannon. 7, 97-111, 1996.
- [11] K. Kuratowski, Topology I, Warszawa, 1933.
- [12] M. Mrsevic, I. L. Reilly and M. K. Vamanamurthy, On semi-regularization topologies, J. Austral. Math. Soc. Ser. A 38 (1), 40-54, 1985.
Abstract
In this paper by using regular open sets and $\Gamma$-local functions, we introduce and investigate the notions of $\mathcal{I}_R$-dense sets, $\mathcal{I}_R$-hyperconnectedness, $\mathcal{I}^*_R$-hyperconnectedness, $\Gamma$-resolbablity and regular $\Gamma$-irresobability in ideal topological spaces.
Keywords
ideal topological space regular open set $R$-hyperconnected $\Gamma$-resolvable regular $\Gamma$-irresolbable $\mathcal{I}_R$-dense
References
- [1] A. Al-Omari, Soft topology in ideal topological spaces, Hacet. J. Math. Stat. 48 (5), 1277-1285, 2019.
- [2] A. Al-Omari and T. Noiri, Local closure functions in ideal topological spaces, Novi Sad J. Math. 43 (2), 139-149, 2013.
- [3] A. Al-Omari and T. Noiri, Local function $\Gamma^{*}$ in ideal topological spaces, Sci. Stud. Res. Ser. Math. Inform. 26 (1), 5-16, 2016.
- [4] A. Al-Omari and T. Noiri, On operators in ideal minimal spaces, Mathematica 58 (81), 3-13, 2016.
- [5] J. Dontchev and M. Ganster, On compactness with respect to countable extensions of ideals and the generalized Banach Category Theorem, Acta. Math. Hungar. 88 (1-2), 53-58, 2000.
- [6] J. Dontchev, M. Ganster and D. Rose, Ideal resolvability, Topology Appl. 93 (1), 1-16, 1999.
- [7] E. Hatir, A. Al-Omari and S. Jafari, $\delta$-Local functions and its properties in ideal topological spaces, Fasc. Math. 53, 53-64, 2014.
- [8] E. Hewitt, A problem of set-theoretic topology, Duke Math. J. 10, 309-333, 1943.
- [9] D. Jankovic and T.R. Hamlett, New topologies from old via ideals, Amer. Math. Monthly 97, 295-310, 1990.
- [10] D. Jankovic and Ch. Konstadilaki, On covering properties by regular closed sets, Math. Pannon. 7, 97-111, 1996.
- [11] K. Kuratowski, Topology I, Warszawa, 1933.
- [12] M. Mrsevic, I. L. Reilly and M. K. Vamanamurthy, On semi-regularization topologies, J. Austral. Math. Soc. Ser. A 38 (1), 40-54, 1985.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | February 14, 2022 |
| Published in Issue | Year 2022 Volume: 51 Issue: 1 |