On some properties of $\mathcal{I}^\mathcal{K}_{sn}$-topological spaces

Ankur Sharmah; Debajit Hazarika

doi:10.5269/bspm.62781

Autores

ANKUR SHARMAH Tezpur University https://orcid.org/0000-0002-3894-642X
Debajit Hazarika Tezpur University

DOI:

https://doi.org/10.5269/bspm.62781

Resumo

In this paper, we introduce the notion of I^K_sn-open set and show that the family of I^K_sn-open sets in a topological space forms a topology. The category of I^K-neighborhood spaces is introduced and several properties are obtained there after. Moreover, we obtain a necessary and sufficient condition for the coincidence of the notions ``preserving I^K-convergence'' and `` I^K-continuity'' for any mapping defined on $X$. Several mappings that are defined on a topological space are shown to be coincident in an I^K-sequential space. The entire investigation is performed in the setting of I^K-convergence which further extends the recent
developments [11,13,1].

Biografia do Autor

ANKUR SHARMAH, Tezpur University

Department of Mathematics
Debajit Hazarika, Tezpur University

Department of Mathematics

Referências

1. A. Sharmah and D. Hazarika, Further aspects of IK-convergence in topological spaces, Appl. Gen. Topol., 22(2)(2021), 355–366.
2. A. Sharmah and D. Hazarika, On covering and quotient maps for IK-convergence in topological space, Preprint, 2021.
3. B.K. Lahiri and P. Das, I and Iâ‹†-convergence of nets, Real Anal. Exchange, 33(2007), 431–442.
4. B. K. Lahiri and P. Das, I and Iâ‹†-convergence in topological spaces, Math. Bohemica, 130(2005), 153–160.
5. M. Macaj and M. Sleziak, IK-convergence, Real Anal. Exchange, 36(2011), 177–194.
6. P. Das, S. Dasgupta, S. Glab, M. Bienias, Certain aspects of ideal convergence in topological spaces, Topology Appl., 2019.
7. P. Das, S. Sengupta, J. Supina, IK-convergence of sequence of functions, Math. Slovaca, 69(5)(2019), 1137–1148.
8. P. Halmos, S. Givant, Introduction to Boolean Algebras, Undergraduate Texts in Mathematics, Springer, New York, 2009.
9. P. Kostyrko, M. Macaj and T. Salat, Statistical convergence and I-convergence, http://thales.doa.fmph.uniba.sk/macaj/ICON.pdf, 1999, Unpublished.
10. P. Kostyrko, T. Salat and W. Wilczynski, I-convergence, Real Anal. Exchange, 26(2001), 669–685.
11. S. Lin, on I-neighborhood spaces and I-quotient spaces, Bull. Malays. Math. Sci. Soc., 44(2021), 1979–2004.
12. S. Lin, L. Liu, G-methods, G-spaces and G-continuity in a topological spaces, Topol. Appl. 22(2016), 29-48.
13. X. Zhou, L. Liu and L. Shou, On topological space defined by I-convergence, Bull. Iranian Math. Soc., 19(2019), 01–18.