Space of infinite subsets of the natural numbers
= Space of infinite subsets of the natural numbers
{title2=$[\mathbb N]^\omega$}
The space $[\mathbb N]^\omega$, also written $\mathbb N^{(\omega)}$, consists of all infinite subsets of the <positive integers>. An element is identified with its strictly increasing enumeration. If $s$ is finite, write $s\sqsubset X$ when $s$ is the finite <initial segment> of this enumeration.