6 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…
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…
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 HubiÄka +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…
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…