Bicompleteness of the fine quasi-uniformity

Künzi, Hans-Peter A.; Ferrario, Nathalie (1991). Bicompleteness of the fine quasi-uniformity. Mathematical proceedings of the Cambridge Philosophical Society, 109(1), pp. 167-186. Cambridge University Press 10.1017/S0305004100069644

[img]
Preview
Text
S0305004100069644.pdf - Published Version
Available under License Publisher holds Copyright.

Download (1MB) | Preview

A characterization of the topological spaces that possess a bicomplete fine quasi-uniformity is obtained. In particular we show that the fine quasi-uniformity of each sober space, of each first-countable T1-space and of each quasi-pseudo-metrizable space is bicomplete. Moreover we give examples of T1-spaces that do not admit a bicomplete quasi-uniformity. We obtain several conditions under which the semi-continuous quasi-uniformity of a topological space is bicomplete and observe that the well-monotone covering quasiuniformity of a topological space is bicomplete if and only if the space is quasi-sober.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Künzi, Hans Peter Albert

Subjects:

500 Science > 510 Mathematics

ISSN:

0305-0041

Publisher:

Cambridge University Press

Language:

English

Submitter:

Marceline Brodmann

Date Deposited:

21 Jul 2020 11:40

Last Modified:

25 Jul 2020 19:20

Publisher DOI:

10.1017/S0305004100069644

BORIS DOI:

10.7892/boris.115455

URI:

https://boris.unibe.ch/id/eprint/115455

Actions (login required)

Edit item Edit item
Provide Feedback