A separable normal nonparacompact space

A topological space X is said to be paracompact [1] if for every open covering G of X there is a locally finite open covering G' of X which is a refinement of G. (G' is locally finite if every point of X has a neighborhood which intersects only a finite number of members of G'.) It is known that every paracompact Hausdorff space is normal [1 ] and that every metrizable space is paracompact [2 ]. Since every normal Hausdorff space with a countable base is metrizable, therefore, every normal Hausdorff space with a countable base is paracompact. The purpose of this paper is to show that the existence of a countable base cannot be replaced by separability in this last statement.