Pelczyński compactum

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The Pelczyński compactum $P$ is a metric compactification of the integers with a Cantor set as the remainder.

Pelczynski compactum.png

Properties

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 $P$.

Proof:

Countably infinite compactum homeomorphic to Pelczyński