Topology Proceedings 27 No. 1 (2003), pp. 111-125

Non-normality numbers

S. Dolecki, T. Nogura, R. Peirone and G. M. Reed

The non-normality number and the strong non-normality number of a topological space are introduced to the effect that a topology is normal if and only if its non-normality number is 1 if and only if its strong non-normality number is 1. It is proved that for every cardinal \kappa, there exists a completely regular topology of non-normality and strong non-normality \kappa; for every uncountable regular cardinal \kappa, there exists a (completely regular) Moore space of non-normality and cardinality \kappa. On the other hand, for every pair of cardinals \kappa < \lambda there exists a completely regular topology of strong non-normality \kappa and non-normality greater than \lambda. As an answer to a question of Umberto Marconi, it is proved that the non-normality number of every separable regular topology with a closed discrete subset of cardinality continuum is at least continuum.

Mathematics Subject Classification: 54D15

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Topology Proceedings, Volume 27 No. 1 (2003)
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