Non normality number
by
Szymon Dolecki
Burgundy University
Coauthors: Tsugunori Nogura (Ehime University), Roberto Peirone (Unviversity of Rome, Tor Vergata)

The non normality number of a topological space X is the supremum of the cardinal numbers for which there exists a family, of that cardinality, of disjoint closed subsets of X such that every finite collection of open supersets of the elements of the family, has non empty intersection. A topology is normal if and only if its non normality number is 1. It is proved that for every cardinal number, there exists a completely regular topology of non normality equal to that cardinal. Answering a question of U. Marconi, it is proved that the non normality number of every separable Hausdorff topology with a closed discrete subset of cardinality continuum, is at least continuum.

Date received: January 14, 2001