5 citations · 6 across the 7 of their papers we have counts for
7 papers
Pointless Parts of Completely Regular Locales
Richard N. Ball
(Completely regular) locales generalize (Tychonoff) spaces; indeed, the passage from a locale to its spatial sublocale is a well understood coreflection. But a locale also possesse…
Structural aspects of truncated archimedean vector lattices: simple elements, good sequences
Richard N. Ball
The truncation operation facilitates the articulation and analysis of several aspects of the structure of archimedean vector lattices; we investigate two such aspects in this artic…
Colored graphs without colorful cycles
Richard N. Ball, Aleš Pultr, Petr Vojtěchovský
A colored graph is a complete graph in which a color has been assigned to each edge, and a colorful cycle is a cycle in which each edge has a different color. We first show that a…
Pointfree pointwise suprema in unital archimedean -groups
Richard N. Ball, Anthony W. Hager, Joanne Walters-Wayland
We generalize the concept of the pointwise supremum of real-valued functions to the pointfree setting. The concept itself admits a direct and intuitive formulation which makes no m…
Truncated Abelian Lattice-Ordered Groups II: the Pointfree (Madden) Representation
Richard N. Ball
This is the second of three articles on the topic of truncation as an operation on divisible abelian lattice-ordered groups, or simply -groups. This article uses the notation…
From Freudenthal's Spectral Theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra
Richard N. Ball, Vincenzo Marra, Daniel McNeill +1
We use a landmark result in the theory of Riesz spaces - Freudenthal's 1936 Spectral Theorem - to canonically represent any Archimedean lattice-ordered group with a strong unit…
Unital hyperarchimedean vector lattices
Richard N. Ball, Vincenzo Marra
We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that,…