Evenly Resolvable Spaces
by
Li Feng
Darton College

In a topological space, a dense subset D is said to be even with a subset E if |D \cap U|=|E \cap U| for every open subset U. A topological space X is evenly resolvable if there is a dense subset D such that D is even with X-D. Let X be a Hausdorff space without isolated points. We show that: (1) if X is locally compact, then X has a dense evenly resolvable subspace; (2) if X is metrizable, then X has a dense evenly resolvable subspace; (3) if X is a resolvable topological group, then X is evenly resolvable; (4) (GCH) if X is Tychonoff and resolvable, then X has a dense evenly resolvable subspace.

Date received: July 20, 1999