Quartz crystal microbalance: Difference between revisions

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The '''Nagata–Smirnov metrization theorem''' in [[topology]] characterizes when a [[topological space]] is [[metrizable]]. The theorem states that a topological space <math>X</math> is metrizable if and only if it is [[regular space|regular]] and has a [[countably locally finite]] (i.e., σ-locally finite) [[basis (topology)|basis]].
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Unlike Urysohn's [[metrization theorem]], which provides only a sufficient condition for metrizability, this theorem provides both a necessary and sufficient condition for a topological space to be metrizable. The theorem is named after [[Jun-iti Nagata|Junichi Nagata]] and Yuriĭ Mikhaĭlovich Smirnov.
 
==See also==
*[[Bing metrization theorem]]
 
==References==
*{{citation|title=Topology|first=James R.|last=Munkres|authorlink=James Munkres|publisher=Prentice Hall|year=1975|isbn=0-13-925495-1|contribution=Sections 6-2 and 6-3|pages=247–253}}.
*{{citation|title=Foundations of Topology|first=C. Wayne|last=Patty|edition=2nd|publisher=Jones & Bartlett|year=2009|isbn=978-0-7637-4234-8|contribution=7.3 The Nagata–Smirnov Metrization Theorem|pages=257–262}}.
 
{{DEFAULTSORT:Nagata-Smirnov metrization theorem}}
[[Category:General topology]]
[[Category:Theorems in topology]]
 
 
{{topology-stub}}

Latest revision as of 07:55, 29 October 2014

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