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
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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) |
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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: |
05 Dec 2022 15:13 |
Publisher DOI: |
10.1017/S0305004100069644 |
BORIS DOI: |
10.7892/boris.115455 |
URI: |
https://boris.unibe.ch/id/eprint/115455 |
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