  Let $\kappa$ be an infinite cardinal. A topological space $X$ is
$\kappa$-bounded if the closure of any subset of cardinality $\le\kappa$ in $X$
is compact. We discuss the problem of embeddability of topological spaces into
Hausdorff (Urysohn, regular) $\kappa$-bounded spaces, and present a canonical
construction of such an embedding. Also we construct a (consistent) example of
a sequentially compact separable regular space that cannot be embedded into a
Hausdorff $\omega$-bounded space.
