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Refining connected topological group topologies on Abelian torsion-free groups. (English) Zbl 0895.54023
The authors develop a technique for refining certain topological groups. The main result of the paper is:
Theorem. Let $$G$$ be a connected Abelian torsion-free group with weight less than or equal to $$\aleph_1$$ and cellularity less than or equal to $$\aleph_0$$. Then $$G$$ admits a strictly finer connected topological group topology satisfying the same cardinality restrictions.
Reviewer: R.Cowen (Gaborone)

##### MSC:
 54H11 Topological groups (topological aspects) 22A05 Structure of general topological groups 54D05 Connected and locally connected spaces (general aspects) 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
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