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