Generalizations of bornological convergence and convergence of partial maps via ideal

TL;DR

This paper extends the concept of convergence for nets of partial maps by introducing ideal-based notions of I-convergence and I*-convergence, broadening the theoretical framework of bornological convergence.

Contribution

It introduces ideal-based generalizations of convergence for nets of partial maps, expanding the existing theoretical framework.

Findings

Defines I-convergence and I*-convergence for nets of partial maps.

Provides a generalized framework for bornological convergence.

Extends classical convergence notions using ideals on directed sets.

Abstract

In this paper using the notion of an ideal I on a directed set, we extend the notion of convergence of nets of partial maps to the notions of I-convergence ( or filter convergence) of nets of partial maps and I*- convergence of nets of partial maps.