episciences.org_2021_1664390772
1664390772
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Logical Methods in Computer Science
18605974
11
28
2017
Volume 13, Issue 4
A Few Notes on Formal Balls
Jean
GoubaultLarrecq
Kok Min
Ng
Using the notion of formal ball, we present a few new results in the theory
of quasimetric spaces. With no specific order: every continuous
Yonedacomplete quasimetric space is sober and convergence Choquetcomplete
hence Baire in its $d$Scott topology; for standard quasimetric spaces,
algebraicity is equivalent to having enough center points; on a standard
quasimetric space, every lower semicontinuous $\bar{\mathbb{R}}_+$valued
function is the supremum of a chain of Lipschitz Yonedacontinuous maps; the
continuous Yonedacomplete quasimetric spaces are exactly the retracts of
algebraic Yonedacomplete quasimetric spaces; every continuous Yonedacomplete
quasimetric space has a socalled quasiideal model, generalizing a
construction due to K. Martin. The point is that all those results reduce to
domaintheoretic constructions on posets of formal balls.
11
28
2017
2021
arXiv:1606.05445
10.48550/arXiv.1606.05445
https://arxiv.org/abs/1606.05445v5
https://arxiv.org/abs/1606.05445v1
10.23638/LMCS13(4:18)2017
https://lmcs.episciences.org/2021

https://lmcs.episciences.org/4100/pdf