Singular Hereditary Characters of Points in Countably Tight Compact Spaces
by
Piotr Koszmider
Auburn University

Fedorchuk's space is a countably tight space which is not sequential because it does not have a convergent sequence because each of its points has character \omega₁ relative to any closed subspace that contains this point as a nonisolated point. For every cardinal \lambda of uncountable cofinality we consitently construct a countably tight compact space where there is a point which has character \lambda in every closed subspace that contains this point as a nonisolated point. This provides new reasons why the Moore-Mrowka conjecture mail fail in a compact space. Together with Nyikos' result concerning regular cardinals these constructions also fully characterize possible characters of points in countably tight compact spaces.

Date received: April 12, 1996

Copyright © 1996 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 # caae-48.