# Pelczyński compactum

The Pelczyński compactum $P$ is a metric compactification of the integers with a Cantor set as the remainder.
Theorem: Let $(X,\tau)$ be zero-dimensional, infinite compactum such that the set $\mathscr{I}(X)$ is dense in $X$. Then $2^X$ is homeomorphic to the Pelczyński compactum $P$.