Abstract: | Properties of an order topology in vector lattices and Boolean algebras are studied. The main result is the following: in
a vector lattice or a Boolean algebra with the condition of “closure by one step” (a generalization of the well-known “regularity”
property of Boolean algebras and K-spaces) the order topology is induced by the topology of its Dedekind completion. Bibliography:
4 titles.
Translated fromProblemy Matematicheskogo Analiza, No. 16, 1997, pp. 204–207. |