Lindelof Space

Definition

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

Facts

Consider a Lindelof space $(X,\mathcal{T})$. Then, $X$ is Countably Compact if and only if $X$ is Compact

Every Second-Countable Space is a Lindelof space.