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Difference between revisions of "Pseudo-metric space"

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A set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075740/p0757401.png" /> endowed with a [[Pseudo-metric|pseudo-metric]]. Each pseudo-metric space is normal (cf. [[Normal space|Normal space]]) and satisfies the [[First axiom of countability|first axiom of countability]]. The [[Second axiom of countability|second axiom of countability]] is satisfied if and only if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075740/p0757402.png" /> is separable.
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A set $X$ endowed with a [[Pseudo-metric|pseudo-metric]]. Each pseudo-metric space is normal (cf. [[Normal space|Normal space]]) and satisfies the [[First axiom of countability|first axiom of countability]]. The [[Second axiom of countability|second axiom of countability]] is satisfied if and only if $X$ is separable.
  
  

Revision as of 18:49, 16 April 2014

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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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=31797
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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