Convergence via Filter in Locally Solid Riesz Spaces

Abdullah Aydn

Abstract: Let (E, I) be a locally solid vector lattice. A filter F on the set E is said to be convergent to a vector xaE if, each zero neighborhood set U containing x, U belongs to F. In this paper, we introduce the notion of filter convergence with respect to locally solid topology and study the concept of this convergence and give some basic properties of it.

Keywords: filter convergence, locally solid Riesz space