29 citations · 78 across the 30 of their papers we have counts for
35 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…
Locally solid convergence structures
E. Bilokopytov, J. Conradie, V. G. Troitsky +1
While there is a well developed theory of locally solid topologies, many important convergences in vector lattice theory are not topological. Yet they share many properties with lo…
Atomicity of Boolean algebras and vector lattices in terms of order convergence
Antonio Avilés, Eugene Bilokopytov, Vladimir G. Troitsky
We prove that order convergence on a Boolean algebra turns it into a compact convergence space if and only if this Boolean algebra is complete and atomic. We also show that on an A…
A representation of sup-completion
Achintya Raya Polavarapu, Vladimir G. Troitsky
It was showed by Donner in 1982 that every order complete vector lattice may be embedded into a cone , called the sup-completion of . We show that if one represents the…
Free Banach lattices
T. Oikhberg, M. A. Taylor, P. Tradacete +1
We investigate the structure of the free -convex Banach lattice over a Banach space . After recalling why such a free lattice exists, and giving a convenient f…
Uniformly closed sublattices of finite codimension
Eugene Bilokopytov, Vladimir G. Troitsky
The paper investigates uniformly closed subspaces, sublattices, and ideals of finite codimension in Archimedean vector lattices. It is shown that every uniformly closed subspace (o…