Definition 6

*A topological space is said to be paracompact if it is Hausdorff and satisfies the following axiom:

(PC) Every open covering $\mathscr{R}$ of $X$ has a locally finite open refinement $\mathscr{R}'$. (Set Theory, Chapter II, § 4, no. 6, Definition 5).

Every compact space is clearly paracompact. Every discrete space $X$ is paracompact, for the open covering formed by all sets consisting of a single point of $X$ is locally finite and is finer than every open covering of $X$.