if f : X--> Y is continuous and onto such that X is compact. let g:Y--> Z is a function such that g0f is continuous. prove that g is contiuous. how it can be prceeded.
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Is there an assumption over $\displaystyle X$ like Hausdorff? You can show that $\displaystyle g^{-1}(F)$ is closed for $\displaystyle F$ closed.
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