The inducing condition for the topology of vector lattices from an order completion (Q2714017)

The article is devoted to studying the properties of the ordinal topology for vector lattices and Boolean algebras. The author proves that, in a vector lattice or a Boolean algebra with the ``closing for one step'' property, the ordinal topology is induced by the Dedekind completion. The notion of ``closing for one step'' is a generalization of the well-known regularity property of Boolean algebras and \(K\)-spaces.