compactness and relative compactness

Question

Suppose that $M$ is compact subset of a Banach space X. Is $M$ relatively compact too?

As far as I know, there is a characterisation of compact sets via Hausdorff $\varepsilon$ - net theorem and it's the same for compact and relatively compact sets. So the answer should be positive.

Answer 1

For a subset $S$ of a topological space, being relatively compact means that $\overline S$ is compact. So, if $M$ is compact, then, since $\overline M=M$, which is compact, $M$ is relatively compact too.

Answer 2

I don't know what your definition of 'relatively compact' is but according to the usual definition a set is raltively compact if its closure is compact. Since compact sets are already closed it is obvious that they are also relatively compact.