10.23638/LMCS-13(4:18)2017
https://lmcs.episciences.org/2021
Goubault-Larrecq, Jean
Jean
Goubault-Larrecq
Ng, Kok Min
Kok Min
Ng
A Few Notes on Formal Balls
Using the notion of formal ball, we present a few new results in the theory
of quasi-metric spaces. With no specific order: every continuous
Yoneda-complete quasi-metric space is sober and convergence Choquet-complete
hence Baire in its $d$-Scott topology; for standard quasi-metric spaces,
algebraicity is equivalent to having enough center points; on a standard
quasi-metric space, every lower semicontinuous $\bar{\mathbb{R}}_+$-valued
function is the supremum of a chain of Lipschitz Yoneda-continuous maps; the
continuous Yoneda-complete quasi-metric spaces are exactly the retracts of
algebraic Yoneda-complete quasi-metric spaces; every continuous Yoneda-complete
quasi-metric space has a so-called quasi-ideal model, generalizing a
construction due to K. Martin. The point is that all those results reduce to
domain-theoretic constructions on posets of formal balls.
episciences.org
Mathematics - General Topology
54E99
2017-11-28
2017-11-28
2017-11-28
eng
journal article
arXiv:1606.05445
10.48550/arXiv.1606.05445
1860-5974
https://lmcs.episciences.org/2021/pdf
VoR
application/pdf
Logical Methods in Computer Science
Volume 13, Issue 4
Researchers
Students