Let $f: \mathcal X \to \mathcal Y$ and $g:\mathcal Y \to \mathcal Z$ be maps such that $g \circ f$ is continuous. Then under what condition we can say-(1) $f$ is continuous., (2)-$g$ is continuous?
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I don't think any condition can be said about $f$. Let $g$ be a constant function, then $g \circ f$ is trivially continuous. – Crostul Sep 26 '17 at 21:42
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I'd asked about dependency of continuity of f and g on the continuity of gof. – user381525 Sep 26 '17 at 21:45
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But you have already assumed g as continuous function. – user381525 Sep 26 '17 at 21:46