Ε-net (metric spaces): Difference between revisions

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+#REDIRECT [[Delone set]]
-{{Other uses|Ε-net (disambiguation){{!}}Ε-net}}
+{{R from merge}}
-{{lowercase|title=ε-net (metric spaces)}}
-In the [[mathematics]] of [[metric spaces]], an '''<math>\varepsilon</math>-net''', or '''epsilon net''' relates to having a set which approximates another in the sense that any point in the second set is within a small distance of a point in the first (approximating) set.
-== Definition ==
-An '''{{math|<var>ε</var>}}-net''' is a set of points in a [[metric space]] such that each point of the space is within distance {{math|<var>ε</var>}} of some point in the set. For example, if {{math|<var>ε</var> &gt; 1/2}}, then the integers are an {{math|<var>ε</var>}}-net of the real numbers.
-This should not be confused with the concept of a ''[[net (mathematics)|net]]'', which is equivalent a generalization of the concept of [[sequence]].
-==References==
-*{{cite book | author=Sutherland, W.A. | title=Introduction to metric and topological spaces| publisher=Oxford University Press | year=1975 | isbn=0-19-853161-3 | zbl=0304.54002 | page=110 }}
-{{topology-stub}}
-{{DEFAULTSORT:E-net}}
-[[Category:Metric geometry]]
-[[Category:Mathematical terminology]]
-[[ru:Ε-сеть]]
-[[vi:Lưới ε (không gian metric)]]