Namespaces
Variants
Actions

Difference between revisions of "Pseudo-metric space"

From Encyclopedia of Mathematics
Jump to: navigation, search
(TeX)
(details)
 
Line 1: Line 1:
 
{{TEX|done}}
 
{{TEX|done}}
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.
+
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.
 
 
 
 
 
 
====Comments====
 
 
 
  
 
====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  E. Čech,   "Topological spaces" , Interscience (1966) pp. 532</TD></TR></table>
+
* {{Ref|a1}} E. Čech, "Topological spaces", Interscience (1966) pp. 532

Latest revision as of 14:51, 8 April 2023

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