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.
|[a1]||E. Čech, "Topological spaces" , Interscience (1966) pp. 532|
Pseudo-metric space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo-metric_space&oldid=31797