Suppose \(\Sigma \) is a topological space and \(S(\Sigma )\) is the vector lattice of all equivalent classes of continuous real-valued functions defined on open dense subsets of \(\Sigma \) . In this paper, we establish some lattice and topological aspects of \(S(\Sigma )\) . In particular, as an application, we show that the unbounded order convergence and the order convergence are stable under passing to the Fremlin tensor product of two Archimedean vector lattices.
