3 papers
math.GN2024
Sequences suffice for pointfree uniform completions
Graham Manuell
Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used inste…
math.GN2023
Pointfree topology and constructive mathematics
Graham Manuell
The constructive approach to mathematics has the advantage that witnesses can be extracted from statements of existence and theorems can be unwound to give algorithms. Even better,…
math.RA2022
Congruence frames of frames and -frames
Graham Manuell
We describe the congruence lattices of frames and -frames. We look at the role that congruence biframes play in the category of strictly zero-dimensional biframes and discuss so…