*Definition [#ha01e707] A topological space X is called weakly paracompact if every open cover has a [[point-finite]] open refinement. *Remark [#lf5d4ea5] -It is also called [[metacompact]]. -It is also called [[pointwise paracompact]]. *Reference [#ofdebc35] Lynn Arthur Steen and J. Arthur Seebach, Jr. Counterexamples in Topology, Dover.