View source for Pseudo-metric space

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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====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E. Čech,   "Topological spaces" , Interscience  (1966)  pp. 532</TD></TR></table>