https://en.formulasearchengine.com/api.php?action=feedcontributions&feedformat=atom&user=152.133.8.3formulasearchengine - User contributions [en]2026-05-31T15:59:36ZUser contributionsMediaWiki 1.43.0-wmf.28https://en.formulasearchengine.com/index.php?title=Rapid_shallow_breathing_index&diff=27060Rapid shallow breathing index2013-11-07T11:50:23Z<p>152.133.8.3: /* Measurement */</p>
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<div>{{orphan|date=September 2011}}<br />
In [[topology]] and related areas of [[mathematics]], a '''neighbourhood space''' is a [[set (mathematics)|set]] ''X'' such that for each <math>x \in X</math> there is an associated [[neighbourhood system]] <math>\mathfrak{R}_x</math>. <ref name=mendelson>{{cite book|last=Mendelson|first=Bert|title=Introduction to Topology|year=1975|publisher=Dover|location=New York|isbn=978-0-486-66352-4|pages=77}}</ref> <br />
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A subset O of a neighbourhood space is called ''open'' if for every <math>x \in O</math> is a neighbourhood of x. Under this definition the open sets of a neighbourhood space give rise to a [[topological space]]. Conversely, every topological space is a neighbourhood space under the usual definition of a neighbourhood in a topological space.<ref name=mendelson /><br />
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==See also==<br />
*[[Neighbourhood (mathematics)|neighbourhood]]<br />
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==References==<br />
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{{DEFAULTSORT:Neighbourhood System}}<br />
[[Category:General topology]]</div>152.133.8.3