Vol. 75, No. 2, 1978

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Normal subspaces of the density topology

Franklin D. Tall

Vol. 75 (1978), No. 2, 579–588

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 .)

Mathematical Subject Classification 2000
Primary: 54D15
Secondary: 28A05, 02K05
Received: 23 November 1976
Revised: 22 April 1977
Published: 1 April 1978
Franklin D. Tall