Extraresolvable Spaces
by
S. Garcia-Ferreira
Coauthors: V. I. Malykhin, A. Tomita

Following Malykhin, we say that a space X is extraresolvable if there is a family { D_\xi : \xi < \Delta(X)⁺ } of dense subsets of X such that D_\xi \cap D_\zeta is nowhere dense whenever \xi < \zeta < \Delta(X)⁺, where \Delta(X) = min{ |V| : \emptyet =/= V subset or equal X  is  open } is the dispersion character of X. Observe that a space X cannot have more that \Delta(X)-many pairwise disjoint dense subsets. It is not hard to see that every extraresolvable space is \omega-resolvable. The real line is \omega-resolvable and is not extraresolvable. We also show that compact metric spaces and compact topological groups are not extraresolvable. We give some examples of metric extraresolvable topological Abelian groups and compact extraresolvable spaces. An example of a pseudocompact extraresolavble topological Abelian group is given.

Date received: July 1, 1997

Copyright © 1997 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 # caao-68.