Continuous function: Difference between revisions

Latest revision as of 22:28, 21 September 2007

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-In [[mathematics]], a [[function]] f from a [[topological space]] <math>(X,O_X)</math> to another topological space <math>(Y,O_Y)</math>, usually written as <math>f:(X,O_X) \rightarrow (Y,O_Y)</math>, is a '''continuous function''' if for every point <math>y \in Y</math> such that <math>y=f(x)</math> for some <math>x \in X</math>,  ''and'' for every [[open set]] <math>U_y \in O_y</math> containing ''y'', there exists an open set <math>U_x \in O_X</math> containing ''x'' such that <math>f(U_x) \subset U_y</math>. Here <math>f(U_x)=\{f(x') \in Y \mid x' \in U_x\}</math>.
+#REDIRECT [[Continuity]]
-[[Category:Mathematics_Workgroup]]
-[[Category:CZ Live]]