Convergent $G_n$-Methods via Nets

Abstract

As a  generalisation of limit notion in topological spaces,  the idea of  $G$-method is  a set valued function defined on a subset of the sequences in a set $X$. Hence $G$-methods   enable  us extending sequential  versions of some topological definitions  such as  sequential continuity, sequential compactness and sequential connectedness. In this paper we consider  the convergent methods defined for nets on $X$, rather than sequences and denote such a method by $G_n$.    Then we also give some properties  and  characterizations of the properties involving the  $G_n$-methods.