1 citations · 1 across the 2 of their papers we have counts for
11 papers
Wallman Duality for Semilattice Subbases
Tristan Bice, Wiesław Kubiś
We extend Wallman's classic duality from lattice bases to semilattice subbases and from compact to locally closed compact spaces. Moreover, we make this duality functorial via appr…
Reconstructing Etale Groupoids from Semigroups
Tristan Bice, Lisa Orloff Clark
We unify various étale groupoid reconstruction theorems such as: 1) Kumjian-Renault's reconstruction from a groupoid C*-algebra. 2) Exel's reconstruction from an ample inverse semi…
Locally Hausdorff Tight Groupoids Generalised
Tristan Bice, Charles Starling
We extend Exel's ample tight groupoid construction to non-ample groupoids, even in the general locally Hausdorff case.
An Algebraic Approach to the Weyl Groupoid
Tristan Bice
We unify the Kumjian-Renault Weyl groupoid construction with the Lawson-Lenz version of Exel's tight groupoid construction. We do this by utilising only a weak algebraic fragment o…
Distance Domains: Continuity
Tristan Bice
We take the abstract basis approach to classical domain theory and extend it to quantitative domains. In doing so, we provide dual characterisations of distance domains (some new e…
Nearness Posets
Tristan Bice
We extend nearness frames to posets representing bases and even subbases of spaces. This allows us to put a classic duality due to Wallman, between compact spaces and a…