Difference between revisions of "Pseudo-metric space"
From Encyclopedia of Mathematics
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| − | A set $X$ endowed with a [[ | + | A set $X$ endowed with a [[pseudo-metric]]. Each pseudo-metric space is normal (cf. [[Normal space]]) and satisfies the [[first axiom of countability]]. The [[second axiom of countability]] is satisfied if and only if $X$ is separable. |
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| − | + | * {{Ref|a1}} E. Čech, "Topological spaces", Interscience (1966) pp. 532 | |
Latest revision as of 14:51, 8 April 2023
A set $X$ endowed with a pseudo-metric. Each pseudo-metric space is normal (cf. Normal space) and satisfies the first axiom of countability. The second axiom of countability is satisfied if and only if $X$ is separable.
References
- [a1] E. Čech, "Topological spaces", Interscience (1966) pp. 532
How to Cite This Entry:
Pseudo-metric space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo-metric_space&oldid=53677
Pseudo-metric space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo-metric_space&oldid=53677
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article