Namespaces
Variants
Actions

Pseudo-metric space

From Encyclopedia of Mathematics
Revision as of 14:51, 8 April 2023 by Chapoton (talk | contribs) (details)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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