Let be a real vector space and be a partial order on this space. The authors give the definition of an ordered vector space as follows:
(i) if and , then for each ,
(ii) if and , then for each
In addition, if is a lattice with respect to the partial ordering, then is said to be a Riesz space (or a vector lattice).
Then they introduce the concepts of statistical topological convergence of a sequence, statistical -boundedness, statistical -Cauchy property, and statistical continuity in a locally solid Riesz space, which was introduced in [G. T. Roberts, Proc. Camb. Philos. Soc. 48, 533–546 (1952; Zbl 0047.10503)]. Moreover, the authors give some results concerning the definitions.