Study of Statistical Convergence of Triple Sequences in a Topological Space

Abstract

In this paper, we introduce statistical convergence of triple sequences which are defined in a topological space. Various results on statistically convergent triple sequences are produced by using the notion of triple natural density operator. Moreover, we initiate the concept of -convergence of triple sequence and establish the interrelationship among -convergence and -converegnce. We see that the first one implies the second one but it’s not vice-versa. But if we restrict the triple sequences to hold the property of first countability, we verify that these notions becomes equivalent. Finally, we prove that the family of all statistically convergent triple sequences under some conditions generates a topological structure within the topological space where they have been defined.

Keywords

• statistical convergence
• triple sequence
• topological space