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Zero-dimensional groups and factorization of homomorphisms with respect to weight and dimension. (English. Russian original) Zbl 0786.22003
Sib. Math. J. 32, No. 3, 477-484 (1991); translation from Sib. Mat. Zh. 32, No. 3(187), 151-159 (1991).
The main result is: Every topological group \(G\) is a factor group of some topological group of dimension zero in the sense of the small inductive dimension which has the same weight as \(G\).
In the second part of the paper it is shown that under certain restrictions on a topological group \(G\) for every continuous homomorphism \(f: G\to H\) there exist a topological group \(G^*\), \(\dim G^*\leq \dim G\) and continuous homomorphisms \(h_ 1: G^*\to H\), \(h_ 2: G\to G^*\), such that \(f=h_ 1 h_ 2\).

MSC:
22A05 Structure of general topological groups
54H11 Topological groups (topological aspects)
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