Statistical order limit points in Riesz spaces

Abstract

The concept of statistical order convergence of sequences in Riesz spaces was introduced and studied. In the present paper, we define the statistical order limit points of a sequence (xn) as a vector x that is the order limit of a subsequence (xk)k is an element of K of (xn) such that the set K does not have density zero. Moreover, we introduce the statistical order cluster points of sequences in Riesz spaces, and also, we give some relations between them.