Countable Compactness

Definition

Consider a Topological Space $(X,\mathcal{T})$. The space is countably compact if every countable open covering (a collection of countable open subsets $\{U_i{\}}_{i\in \mathbb{N}}$ of $X$ whose union is $X$) of $X$ has a finite subcovering.

Facts

Every compact space is Countably Compact.

Link to original