arXiv subjects

Felix Dilke

Publications and source records attributed to Felix Dilke.

2 recordsLinked to original sources

arXiv2018

Graphs, Ultrafilters and Colourability

Let $β$ be the functor from Set to CHaus which maps each discrete set X to its Stone-Cech compactification, the set $β$ X of ultrafilters on X. Every graph G with vertex set V naturally gives rise to a graph $βG$ on the set $βV$ of ultrafilters on V . In what follows, we interrelate the properties of G and $βG$. Perhaps the most striking result is that G can be finitely coloured iff $βG$ has no loops.

math.CT↗

arXiv2018

Injective Hulls In a Locally Finite Topos

We show that in a locally finite topos, every object has an essential extension that is injective, and that this extension is unique up to isomorphism. The construction was motivated by work on Bewl, a software project for doing topos-theoretic calculations.

math.CT↗