The notion of I-convergence was introduced in the paper [KOSTYRKO,P.-ŠALÁT,T.-WILCZYNSKI,W.: I-convergence, Real Anal. Exchange 26 (2000-2001), 669-686]. This notion includes the notion of the statistical convergence which has been intensively investigated in last twenty years. In the present paper we will give some of its basic properties and we will deal with extremal I-limit points.

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This paper is extension of the unpublished manuscript P. Kostyrko, M. Mačaj, T. šalát: Statistical convergence and I-convergence.