Ideal convergence in locally solid Riesz spaces

Abstract

An ideal $I$ is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper, we introduce the concepts of ideal $\tau$-convergence, ideal $\tau$-Cauchy and ideal $\tau$-bounded sequence in locally solid Riesz space endowed with the topology $\tau.$ Some basic properties of these concepts has been investigated. We also examine the ideal $\tau$-continuity of a mapping defined on locally solid Riesz space.