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Keywords:
$I$-convergence; $I^*$-convergence; condition (AP); $I$-limit point; $I$-cluster point
Summary:
We extend the idea of $I$-convergence and $I^*$-convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.
References:
[1] Baláž, V., Červeňanský, J., Kostyrko, P., Šalát, T.: $I$-convergence and $I$-continuity of real functions. Faculty of Natural Sciences, Constantine the Philosoper University, Nitra, Acta Mathematica 5, 43–50.
[2] Connor, J. S.: The statistical and strong $p$-Cesaro convergence of sequences. Analysis 8 (1988), 47–63. MR 0954458 | Zbl 0653.40001
[3] Demirci, K.: $I$-limit superior and limit inferior. Math. Commun. 6 (2001), 165–172. MR 1908336 | Zbl 0992.40002
[4] Fast, H.: Sur la convergence statistique. Colloq. Math. 2 (1951), 241–244. MR 0048548 | Zbl 0044.33605
[5] Halberstem, H., Roth, K. F.: Sequences. Springer, New York, 1993.
[6] Kostyrko, P., Šalát, T., Wilczyński, W.: $I$-convergence. Real Analysis Exch. 26 (2000/2001), 669–685. MR 1844385
[7] Kostyrko, P., Mačaj, M., Šalát, T., Sleziak, M.: $I$-convergence and a termal $I$-limit points. (to appear).
[8] Kuratowski, K.: Topologie I. PWN, Warszawa, 1962.
[9] Lahiri, B. K., Das, Pratulananda: Further results on $I$-limit superior and $I$-limit inferior. Math. Commun. 8 (2003), 151–156. MR 2026393
[10] Mačaj M., Šalát, T.: Statistical convergence of subsequences of a given sequence. Math. Bohem. 126 (2001), 191–208. MR 1826482
[11] Niven, I., Zuckerman, H. S.: An introduction to the theory of numbers. 4th ed., John Wiley, New York, 1980. MR 0572268
[12] Šalát, T.: On statistically convergent sequences of real numbers. Math. Slovaca 30 (1980), 139–150. MR 0587239
[13] Šalát, T., Tripathy, B. C., Ziman, M.: A note on $I$-convergence field. (to appear). MR 2203460
[14] Schoenberg, I. J.: The integrability of certain function and related summability methods. Am. Math. Mon. 66 (1959), 361–375. MR 0104946
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