Difficult# Topological Equivalence, Convergence, Compactness

TOPO-FLHVZK

Let $(X,d)$ be a metric space. A set $K\subset X$ is called *(sequentially) relatively compact* if every sequence $(x_n)_n$ in $X$ entirely contained in $K$ has a converging subsequence.

If, in addition, all such subsequential limits are also contained in $K$, then $K$ is said to be a *(sequentially) compact* subset of $X$.

Choose **ALL** the statements from the list which must be true: