4 papers · 1 filter
Order convergence in ordered vector spaces: compactness, atoms, pervasiveness, and ice cream spaces
Eugene Bilokopytov, Mark Roelands, Samuel Tiersma +3
We study order convergence in ordered vector spaces that are not necessarily lattices. In this setting, we consider two generalizations of order convergence on vector lattices, a d…
The Dedekind completion of an Archimedean ordered vector space as a reflector
Antonio Avilés, Eugene Bilokopytov
We consider the category of Archimedean ordered vector spaces with linear maps which preserve all existing suprema, and its full subcategories , $\m…
Normed lattices majorizing in their norm completions
Eugene Bilokopytov, Viktor Bohdanskyi
This note is a follow-up to \cite{bt}. We focus on conditions under which a normed lattice is majorizing in its norm completion. We show that \cite[Question 8.17]{bt} -- namely…
Relative uniform completion of a vector lattice
Eugene Bilokopytov, Vladimir G. Troitsky
In the paper, we revisit several approaches to the concept of uniform completion of a vector lattice . We show that many of these approaches yield the same res…