  What topological spaces can be partitioned into copies of the Cantor space
$2^\omega$? An obvious necessary condition is that a space can be partitioned
into copies of $2^\omega$ only if it can be covered with copies of $2^\omega$.
We prove three theorems concerning when this necessary condition is also
sufficient.
  If $X$ is a metrizable space and $|X| \leq \mathfrak{c}^{+\omega}$ (the least
limit cardinal $>\!\mathfrak{c}$), then $X$ can be partitioned into copies of
$2^\omega$ if and only if $X$ can be covered with copies of $2^\omega$. To show
this cardinality bound is sharp, we construct a metrizable space of size
$\mathfrak{c}^{+(\omega+1)}$ that can be covered with copies of $2^\omega$, but
not partitioned into copies of $2^\omega$.
  Similarly, if $X$ is first countable and $|X| \leq \mathfrak{c}$, then $X$
can be partitioned into copies of $2^\omega$ if and only if $X$ can be covered
with copies of $2^\omega$. On the other hand, there is a first countable space
of size $\mathfrak{c}^+$ that can be covered with copies of $2^\omega$, but not
partitioned into copies of $2^\omega$.
  Finally, we show that a completely metrizable space can be partitioned into
copies of $2^\omega$ if and only if it can be covered with copies of $2^\omega$
if and only if it has no isolated points.
