  In this paper a generalization of Urysohn's metrization theorem is given for
higher cardinals. Namely, it is shown that a topological space with a basis of
cardinality at most $|\omega_\mu|$ or smaller is $\omega_\mu$-metrizable if and
only if it is $\omega_\mu$-additive and regular, or, equivalently,
$\omega_\mu$-additive, zero-dimensional, and T\textsubscript{0}. Furthermore,
all such spaces are shown to be embeddable in a suitable generalization of
Hilbert's cube.
