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The union of resolvable spaces is resolvable. (English) Zbl 0769.54002

Summary: Following E. Hewitt [Duke Math. J. 10, 309-333 (1943; Zbl 0060.394)], a space is said to be resolvable if it admits complementary, dense subsets.
Theorem: Let \(X=\bigcup_{i\in I} X_ i\) with each \(X_ i\) resolvable in the subspace topology. Then \(X\) itself is resolvable .
Corollary: A homogeneous space with a non-empty resolvable subspace is resolvable.

MSC:

54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54H11 Topological groups (topological aspects)
22A05 Structure of general topological groups
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