6 papers
Effective quasi-Polish categories of overt discrete spaces and compact Hausdorff spaces
Matthew de Brecht
We construct the category of overt discrete quasi-Polish spaces and the category of compact Hausdorff quasi-Polish spaces (and some of their subcategories) as internal categories o…
On the completeness of the countable fragment of geometric logic
Matthew de Brecht
We give self contained proofs of the completeness of countable -coherent theories, for both propositional and predicate logic. By -coherent logic we mean the fragment of geom…
A note on computable étale spaces
Matthew de Brecht
An étale space over a topological space is defined as a local homeomorphism from a topological space into . They often come up in topos theory because of the equivalence…
Constructing the space of valuations of a quasi-Polish space as a space of ideals
Matthew de Brecht
We construct the space of valuations on a quasi-Polish space in terms of the characterization of quasi-Polish spaces as spaces of ideals of a countable transitive relation. Our con…
Some notes on spaces of ideals and computable topology
Matthew de Brecht
We show some basic results on the characterization of quasi-Polish spaces in terms of spaces of ideals, with an emphasis on the connections with computable topology.
Domain-complete and LCS-complete spaces
Matthew de Brecht, Jean Goubault-Larrecq, Xiaodong Jia +1
We study subspaces of continuous dcpos, which we call domain-complete spaces, and subspaces of locally compact sober spaces, which we call LCS-complete spaces. Those in…