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Exactly $$n$$-resolvable spaces and $$\omega$$-resolvability. (English) Zbl 0998.54026
Summary: We show that any topological space has a decomposition into a union of an open $$\omega$$-resolvable subset and the closure of a countable union of pairwise disjoint open sets each of which, when nonempty, is an $$OE_nR$$ space. We present several applications, including characterizations of $$E_nR$$ and $$OE_nR$$ spaces. We also present the construction of a compact Hausdorff space which is the union of a pair of disjoint irresolvable dense subsets, but which is, nevertheless, $$2^{\mathfrak c}$$-resolvable. Indeed, the space constructed is card-homogeneous and maximally resolvable in the sense of J. G. Ceder [Fundam. Math. 55, 87-93 (1964; Zbl 0139.40401)].

##### MSC:
 54F65 Topological characterizations of particular spaces 54B15 Quotient spaces, decompositions in general topology 54D99 Fairly general properties of topological spaces 54D80 Special constructions of topological spaces (spaces of ultrafilters, etc.) 54G20 Counterexamples in general topology