# Pseudo-metric space

From Encyclopedia of Mathematics

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