4 papers
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…
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…
Countability conditions in locally solid convergence spaces
Eugene Bilokopytov, Viktor Bohdanskyi, Jan Harm van der Walt
We study (strong) first countability of locally solid convergence structures on Archimedean vector lattices. Among other results, we characterise those vector lattices for which re…