Non normality numbers
by
Tsugunori Nogura
Ehime University(Matsuyama)
Coauthors: Szymon Dolecki (University of Burgundy), Robert Peirone (University of Rome ``Tor Vergata'')

Two non normality numbers of a topological space are introduced. A topological space is normal if and only if its non normality number is 1 if and only if its strongly non normality number is 1. It is proved that for every cardinal \kappa, there exists a completely regular space of non normality \kappa. On the other hand, for every cardinal \kappa < \lambda there exists a completely regular space of strongly non normality \kappa and non normality greater than \lambda. Answering a question of U. Marconi, it is proved that the non normality number of every separable Hausdorff space with a closed discrete subset of cardinaliy continuum, is at least continuum.

Date received: July 6, 2001