$(X, \tau_X) $ and $(Y, \tau_Y) $ be two topological spaces. $\forall f\in Y^X$ with $\text{Gr}(f) $ is closed implies $f\in C(X, Y) $. Question : Does this implies $(Y, \tau_Y) $ is compact? Notation: $Y^X$: Set of all functions from $X$ to $Y$. $C(X, Y) =\{f\in Y^X: f \text{ is continuous }\}$...