| Autor: |
Jean Goubault-Larrecq, Kok Min Ng |
| Jazyk: |
angličtina |
| Rok vydání: |
2017 |
| Předmět: |
|
| Zdroj: |
Logical Methods in Computer Science, Vol Volume 13, Issue 4 (2017) |
| Druh dokumentu: |
article |
| ISSN: |
1860-5974 |
| DOI: |
10.23638/LMCS-13(4:18)2017 |
| Popis: |
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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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