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Some remarks on Doitchinov completeness

✍ Scribed by Hans-Peter A. Künzi; Salvador Romaguera

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
721 KB
Volume
74
Category
Article
ISSN
0166-8641

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✦ Synopsis

We observe that the well-monotone (open covering) quasiuniformity of each topological space is left K-complete. On the other hand, we exhibit an example of a topological space the fine quasiuniformity of which is not D-complete. The semicontinuous quasiuniformity of a countably metacompact space X is shown to be D-complete if and only if X is closed-complete. Moreover it is proved that the well-monotone quasiuniformity of a ccc regular space X is D-complete if and only if X is almost realcompact.

We also note that a metrizable space admits a D-complete quasimetric if and only if it is an F~set in every metric space in which it is embedded. Each (Tychonoff) (~ech complete quasimetrizable space is shown to admit a left K-complete quasimetric.

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