I-Convergence Classes of Sequences and Nets in Topological Spaces

Abstract

In this paper we have used the idea of I-convergence of sequences and nets to study certain conditions of convergence in a topological space. It has been shown separately that a class of sequences and a class of nets in a non-empty set X which are respectively called I-convergence class of sequences and I-convergence class of nets satisfying these conditions generate a topology on X. Further we have correlated the classes of I-convergent sequences and nets with respect to these topologies with the given classes which satisfy these conditions.

Key words and phrases. ideal, filter, net, I-convergence, I-convergence class, I-cluster point, I-limit space.

2000 Mathematics Subject Classification. Primary 54A20, Secondary 40A35