48 citations · 112 across the 21 of their papers we have counts for
13 papers · 1 filter
On Weakly Hausdorff Spaces and Locally Strongly Sober Spaces
Jean Goubault-Larrecq
We show that the locally strongly sober spaces are exactly the coherent sober spaces that are weakly Hausdorff in the sense of Keimel and Lawson. This allows us to describe their S…
Continuous R-valuations
Jean Goubault-Larrecq, Xiaodong Jia
We introduce continuous -valuations on directed-complete posets (dcpos, for short), as a generalization of continuous valuations in domain theory, by extending values of continu…
A cone-theoretic barycenter existence theorem
Jean Goubault-Larrecq, Xiaodong Jia
We show that every continuous valuation on a locally convex, locally convex-compact, sober topological cone has a barycenter. This barycenter is unique, and the bary…
Infinitary Noetherian Constructions II. Transfinite Words and the Regular Subword Topology
Jean Goubault-Larrecq, Simon Halfon, Aliaume Lopez
We show that the spaces of transfinite words, namely ordinal-indexed words, over a Noetherian space, is also Noetherian, under a natural topology which we call the regular subword…
Statures and Sobrification Ranks of Noetherian Spaces
Jean Goubault-Larrecq, Bastien Laboureix
There is a rich theory of maximal order types of well-partial-orders (wpos), pioneered by de Jongh and Parikh (1977) and Schmidt (1981). Every wpo is Noetherian in its Alexandroff…
Probabilistic Powerdomains and Quasi-Continuous Domains
Jean Goubault-Larrecq
The probabilistic powerdomain on a space is the space of all continuous valuations on . We show that, for every quasi-continuous domain , is a…