Statistical Convergence of Double Sequences

Abstract

In this paper, we show that a double sequence in a topological space satisfies certain conditions, which are capable of generating a topology on a nonempty set. Also, we used the idea of statistical limit and statistical cluster point to establish some properties in the sense of double sequences. One of our main interest is to investigate the relationship between statistical limit, s-limit and statistical cluster points of double sequences.

Key words and phrases. statistical convergence, s-limit, F_σ-set, separable space, double sequence.

2000 Mathematics Subject Classification. 54A20, 40A35, 40A05