5 citations · 10 across the 6 of their papers we have counts for
7 papers
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…
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,…
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…
Uniform locales and their constructive aspects
Graham Manuell
Much work has been done on generalising results about uniform spaces to the pointfree context. However, this has almost exclusively been done using classical logic, whereas much of…
The congruence biframe as a quasi-uniform bicompletion
Graham Manuell
Künzi and Ferrario have shown that a space is sober if and only if it is bicomplete in the well-monotone quasi-uniformity. We prove a pointfree version of this result: a stri…
Strictly zero-dimensional biframes and a characterisation of congruence frames
Graham Manuell
Strictly zero-dimensional biframes were introduced by Banaschewski and Brümmer as a class of strongly zero-dimensional biframes including the congruence biframes. We consider the c…
A special class of congruences on -frames
Graham Manuell
Madden has shown that in contrast to the situation with frames, the smallest dense quotient of a -frame need not be Boolean. We characterise these so-called d-reduced -frames…