Graph of a Continous function

by SiddharthM
Tags: continous, function, graph
 P: 47 I just want to ask that what you have shown is it also a proof of the following or not? If not can you help me with this please. We define: a function $f:M\to N$ between two metric spaces specifies compactness if it has the property $K\subset M$ is compact $\Leftrightarrow \left\{(k,f(k))|k\in K \right\}\subset M\times N$ is compact. Then $f$ specifies compactness $\Leftrightarrow$ $f$ is continuous.