RESOLVABILITY OF TOPOLOGICAL SPACES
I. Juhász
(A. Rényi Inst. of Math.)
A topological space X is said to be k-resolvable (for k a finite or infinite cardinal
number) if X contains k disjoint dense subsets. Most ”nice” spaces (e.g. metric,
or compact, or linearly ordered ones) are maximally resolvable in a precise sense.
But there are countable regular (hence nice) spaces that are irresolvable, i.e. not
2-resolvable.
The aim of this talk is to review several recent results concerning this concept.
We describe joint work with L. Soukup and Z. Szentmiklóssy about a method that
enables us to construct spaces with a large variety of resolvability properties. Then
we present very recent joint work with M. Magidor about a purely set theoretic
characterization of maximal resolvability of monotonically normal spaces, a natural
class of spaces that includes both metric and linearly ordered ones.
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