Disjoint cylinder decomposition of open subsets of Cantor space
= Disjoint cylinder decomposition of open subsets of Cantor space
Every <open set> in <Cantor space> is a countable disjoint union of prefix <cylinder sets>. Select all finite words whose cylinder lies in the open set but whose immediate predecessor's cylinder does not. These words are prefix-free, so their cylinders are disjoint. Every point of the open set has a shortest qualifying prefix. The whole space is represented by the empty prefix.