Products of Michael Spaces and Completely Metrizable Spaces
by
Dennis Burke
Miami University
Coauthors: Roman Pol

For disjoint subsets A, C of [0, 1] the Michael space M(A, C)=A \cup C has the topology obtained by isolating the points in C and letting the points in A retain the neighborhoods inherited from [0, 1]. We study normality of the product of Michael spaces with complete metric spaces. There is a ZFC example of a Lindelöf Michael space M(A, C), of minimal weight \aleph₁, with M(A, C)×B(\aleph₀) Lindelöf but with M(A, C)×B(\aleph₁) not normal. If M(A) denotes M(A, [0, 1]\smallsetminus A), the normality of M(A)×B(\aleph₀) implies the normality of M(A)×S for any complete metric space S (of arbitrary weight). However, the statement ``M(A, C)×B(\aleph₁) normal implies M(A, C)×B(\aleph₂) normal'' is axiom sensitive.

Date received: February 5, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caas-29.