Geodesic
On the uniqueness of $ \mathcal{I}$-limits of sequences
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 744-757

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We define the $ \mathcal{I} $-sequential topology on a topological space where $ \mathcal{I} $ denotes an ideal of the set of positive integers. We also study the relationship between $ \mathcal{I}$-separatedness and uniqueness of $ \mathcal{I}$-limits of sequences. Furthermore, we give a characterization of uniqueness of $ \mathcal{I}$- limits of sequences by $ \mathcal{I}$-closedness of sequentially $ \mathcal{I}$-compact subset.
Keywords: $ \mathcal{I}$-convergence, $ \mathcal{I}$-sequential topology, $ \mathcal{I}$-separated, sequentially $ \mathcal{I}$-compact, $ \mathcal{I}$-bounded, sequentially $ \mathcal{I}$-continuity. 
@article{SEMR_2021_18_2_a27,
     author = {A. Blali and A. El Amrani and R. A. Hassani and A. Razouki},
     title = {On the uniqueness of $ \mathcal{I}$-limits of sequences},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {744--757},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a27/}
}
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A. Blali; A. El Amrani; R. A. Hassani; A. Razouki. On the uniqueness of $ \mathcal{I}$-limits of sequences. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 744-757. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a27/