Definition of One-point compactification

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My question is an elementary one but I can't seem to find the formal definition.
If $M$ and $N$ are topological spaces and $\dot{M}$ is the one-point compactification of $M$ then how is a map $f:M \rightarrow N$ precesely lifted to a map $\dot{f}:\dot{M} \rightarrow \dot{N}$?