The density topology on
the real llne is a strengthening of the usual Euclidean topology which is
intimately connected wilh the measure-theoretic structure. The space itself is
not normal; we are interested in characterizing its normal subspaces. This
leads us to the consideration of various set-theoretic axioms, and yields a
consistent example of a homogeneous normal non-collectionwise Hausdorff
space and indeed a general method for producing normal non-collectionwise
Hausdorff spaces. (A space is collectionwise Hausdorff if for each closed discrete
subset Y there exisl pairwise disjoint open sets, one about each element of
Y .)
