|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
A Few Notes on Formal Balls | | Jean Goubault-Larrecq
; | | Date: |
17 Jun 2016 | | Abstract: | Using the notion of formal ball, we present a few easy, 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 $ar{mathbb{R}}_+$-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; every continuous valuation on a continuous
Yoneda-complete quasi-metric space extends to a Borel measure, and is a
directed supremum of simple valuations. The point is that all those results
reduce to domain-theoretic constructions on posets of formal balls. | | Source: | arXiv, 1606.5445 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER