Gleason's theorem: Difference between revisions

Latest revision as of 14:34, 8 January 2015

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-In [[mathematics]], the '''''ε''-neighborhood''' (or '''epsilon-neighborhood''') of a [[set (mathematics)|set]] ''A''&nbsp;⊆&nbsp;''M'', where (''M'',&nbsp;''d'') is a [[metric space]], is the set of all points of ''M'' whose distance to some point of ''A'' is less than ''ε''&nbsp;&gt;&nbsp;0.<ref name=Barile>{{cite web|last=Barile, Margherita and Weisstein, Eric W.|title=Neighborhood|url=http://mathworld.wolfram.com/Neighborhood.html|publisher=MathWorld|accessdate=21 September 2013}}</ref>  It is customarily denoted by ''A''<sup>''ε''</sup>.  One may write
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-:<math>A^{\varepsilon} := \{ p \in M | \exists q \in A \mathrm{\,s.t.\,} d(p, q) < \varepsilon \} = \bigcup_{p \in A} B_{\varepsilon} (p)</math>
-where ''B''<sub>''ε''</sub>(''p'') is the [[open ball]] of radius ''ε'' centered at a point ''p'' of ''M''.
-==References==
-{{reflist}}
-{{DEFAULTSORT:Epsilon-Neighborhood}}
-[[Category:General topology]]
-[[Category:Metric geometry]]

Gleason's theorem: Difference between revisions

Latest revision as of 14:34, 8 January 2015

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