Statistical convergence of nets on locally solid Riesz spaces

TL;DR

This paper extends the concept of statistical convergence to nets in locally solid Riesz spaces, introducing statistically topological convergence and statistical continuity using topology-free techniques.

Contribution

It introduces statistically topological convergence and statistical continuity for nets in locally solid Riesz spaces, advancing the theoretical framework.

Findings

Defines statistically topological convergence for nets

Introduces statistical continuity in locally solid Riesz spaces

Develops topology-free techniques for these concepts

Abstract

The statistical convergence is handled for sequences with the natural density, in general. In a recent paper, the statistical convergence for nets in Riesz spaces has been studied and investigated by developing topology-free techniques in Riesz spaces. In this paper, we introduce the statistically topological convergence for nets on locally solid Riesz spaces with solid topologies. Moreover, we introduce the statistical continuity on locally solid Riesz spaces.