On spaces in which the norm convergence coincides with the order convergence

Autor: Vulikh, B. Z., Korsakova, O. S.
Zdroj: Mathematical Notes; February 1973, Vol. 13 Issue: 2 p158-163, 6p
Abstrakt: We investigate partially ordered normed vector spaces in which the norm convergence coincides with the order convergence. We consider spaces where the convergences coincide for arbitrary nets and spaces where the convergences coincide only for sequences. We give conditions which characterize such spaces and investigate their properties. In particular, we study the problem of their Dedekind completeness and s-completeness.
Databáze: Supplemental Index
Externí odkaz: