# If \$ f: X times Y to mathbb {R} \$ is continuous and \$ X \$ compact, is \$ and mapsto sup_x f (x, y) \$ continuous?

Suppose $$X, Y$$ they are metrically spaced and $$X$$ compact. Yes $$f: X times Y to mathbb {R}$$ it is continuous, it is $$y mapsto sup_ {x in X} f (x, y)$$ A continuous function?