Based continuous map: Difference between revisions

Latest revision as of 17:57, 19 January 2011

Definition

Suppose $(X,x_{0})$ and $(Y,y_{0})$ are based topological spaces. A based continuous map $f:(X,x_{0})\to (Y,y_{0})$ is a continuous map $f:X\to Y$ with the property that $f(x_{0})=y_{0}$ .

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	==Definition==		==Definition==

	Suppose <math>(X,x_0)</math> and <math>(Y,y_0)</math> are [[defining ingredient::based topological space]]s. A '''based continuous map''' <math>f:(X,x_0) \to (Y,y_0)</math> is a [[continuous map]] <math>f:X \to Y</math> with the property that <math>f(x_0) = y_0</math>.		Suppose <math>(X,x_0)</math> and <math>(Y,y_0)</math> are [[defining ingredient::based topological space]]s. A '''based continuous map''' <math>f:(X,x_0) \to (Y,y_0)</math> is a [[defining ingredient::continuous map]] <math>f:X \to Y</math> with the property that <math>f(x_0) = y_0</math>.