On the lexicographic product of ordered sets
Vítězslav Novák · Czechoslovak Mathematical Journal · 1965
In this paper there is proved the necessary and sufficient condition for the lexicographic product of ordered sets over an ordered set to be an ordered set.The well extension of an ordered set is defined and the necessary and sufficient condition for the existence of a well extension of an ordered set is proved.A certain calculation of the dimension of the lexicographic product of ordered sets is obtained.Especially the dimension of the ordinal product of ordered sets is determined. THE LEXICOGRAPHIC PRODUCT OF ORDERED SETS