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Surjective continuous maps

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Let be a surjective continuous map between topological spaces. Show that:

a) If f is an identification mp, then for any pace Z and any map the composition is continuous if and only if g is continuous.
b) If, for any space Z and any map , the composition is continuous if and only if g is continuous, then f is an identification map.
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Solution Summary

This is a proof regarding a surjective continuous map.

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