On perfectly normal compacta
by
Jacek Nikiel
American University of Beirut
Coauthors: D. Daniel, L.B. Treybig, H.M. Tuncali, E.D. Tymchatyn

Existence of almost all known perfectly normal compact spaces depends on additional set-theoretic conditions, like the negation of the Souslin hypothesis or the continuum hypothesis. Several outstanding open problems ask if it is possible to consistently eliminate all peculiar looking examples.

I will give a brief survey of the topic and show new approaches, results and problems concerning it. Most attention will be spent on the 1982 question of M.E. Rudin about perfectly normal and locally connected compact spaces. Inverse limits of metrizable compact spaces will be used to describe and examine the internal structure of perfectly normal compacta.

Date received: June 30, 2000