18 citations · 103 across the 34 of their papers we have counts for
38 papers
Steinberg Algebras of Ample Semicategories and their Boolean-Cartan Restriction Semigroups
Tristan Bice, Malcolm Jones, Ganna Kudryavtseva
We extend the construction of Steinberg algebras of ample groupoids to étale semicategories. We also relate ample semicategories to Boolean restriction semigroups via a representat…
Dependent Types Simplified
Tristan Bice
We present two logical systems based on dependent types that are comparable to ZFC, both in terms of simplicity and having natural set theoretic interpretations. Our perspective is…
Oscillation stability by the Carlson-Simpson theorem
Tristan Bice, Noé de Rancourt, Jan Hubička +1
We prove oscillation stability for the Banach space : every weak-* Borel, uniformily continuous map from the unit sphere of this space to a compact metric space can be…
Homeomorphisms of the Pseudoarc
Tristan Bice, Maciej Malicki
We construct homeomorphisms of compacta from relations between finite graphs representing their open covers. Applied to the pseudoarc, this yields simple Fraïssé theoretic proofs o…
Generic Compacta from Relations between Finite Graphs: Theory Building and Examples
Adam Bartoš, Tristan Bice, Alessandro Vignati
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relation…
Constructing Compacta from Posets
Adam Bartoš, Tristan Bice, Alessandro Vignati
We develop a simple method of constructing topological spaces from countable posets with finite levels, one which applies to all second countable T_1 compacta. This results in a du…
Big Ramsey degrees in the metric setting
Tristan Bice, Noé de Rancourt, Jan Hubička +1
Oscillation stability is an important concept in Banach space theory which happens to be closely connected to discrete Ramsey theory. For example, Gowers proved oscillation stabili…
The weak Ramsey property and extreme amenability
Adam Bartoš, Tristan Bice, Keegan Dasilva Barbosa +1
We extend the Kechris--Pestov--Todorčević correspondence to weak Fra\"ıssé categories and automorphism groups of generic objects. The new ingredient is the weak Ramsey property. We…
Dauns-Hofmann-Kumjian-Renault Duality for Fell Bundles and Structured C*-Algebras
Tristan Bice
We unify the classic Dauns-Hofmann representation with Kumjian and Renault's Weyl groupoid representation. More precisely, we use ultrafilters to represent C*-algebras with some ad…
Noncommutative Pierce Duality between Steinberg Rings and Ample Ringoid Bundles
Tristan Bice
Classic work of Pierce and Dauns-Hofmann shows that biregular rings are dual to simple ring bundles over Stone spaces. We extend this duality to Steinberg rings, a purely algebraic…
Representing Structured Semigroups on Etale Groupoid Bundles
Tristan Bice
We examine a semigroup analogue of the Kumjian-Renault representation of C*-algebras with Cartan subalgebras on twisted groupoids. Specifically, we show how to represent semigroups…
Lattice-Free and Point-Free: Vickers Duality for Subbases of Stably Locally Compact Spaces
Tristan Bice, Wieslaw Kubis
Inspired by classic work of Wallman and more recent work of Jung-Kegelmann-Moshier and Vickers, we show how to encode general subbases of stably locally compact spaces via certain…
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…
Hausdorff Tight Groupoids Generalised
Tristan Bice, Charles Starling
We extend Exel's ample tight groupoid construction to general locally compact étale groupoids in the Hausdorff case. Moreover, we show how inverse semigroups are represented in thi…
General Non-Commutative Locally Compact Locally Hausdorff Stone Duality
Tristan Bice, Charles Starling
We extend the classical Stone duality between zero dimensional compact Hausdorff spaces and Boolean algebras. Specifically, we simultaneously remove the zero dimensionality restric…
Standard homogeneous C*-algebras as compact quantum metric spaces
Konrad Aguilar, Tristan Bice
Given a compact metric space X and a unital C*-algebra A, we introduce a family of seminorms on the C*-algebra of continuous functions from X to A, denoted C(X, A), induced by clas…
C*-Algebras With and Without -Increasing Approximate Units
Tristan Bice, Piotr Koszmider
For elements of a C*-algebra we denote by . We show that all -unital C*-algebras have -increasing approximate units, extending a classical result fo…
C*-Algebra Distance Filters
Tristan Bice, Alessandro Vignati
We use non-symmetric distances to give a self-contained account of C*-algebra filters and their corresponding compact projections, simultaneously simplifying and extending their ge…
Distance Domains: Completeness
Tristan Bice
We explore extensions of domain theoretic concepts, replacing transitive relations with general non-symmetric distances. These lead to a generalization of Smyth completeness which…