$f:X\rightarrow Y$ is continous map between metric spaces, $K_n$ are non empty nested sequence of compact subsets of $X$, then we need to show the title above.
Please tell me which result I should apply here? regarding cont map and compact set I know that image of compact set is compact, attains bounds, uniformly continous etc. please help. well, we can start by taking $y\in \bigcap f(K_n)$ and then show that it is also in the left side?