# Fundamental group question

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Simple question: is the fundamental group of a pointed space independant of the base point?

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If the space is path connected. Then if $\gamma$ is a path from x1 to x0, the map sending the homotopy class of a loop $\alpha$ in $\pi_1(X,x_0)$ to the homotopy class of the loop $\gamma \alpha \gamma^{-1}$ in $\pi_1(X,x_1)$is easily shown to be an isomorphism.

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