J. van Mill
- Topological groups with a bc-base
- Topology and its Applications
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
Approximately 10 years ago, Zambakhidze asked whether every non-zero-dimensional topological group with a bc-base is locally compact. Below we show that the small inductive dimension ind of any non-locally compact group with such a base doesn't exceed 1. We prove, however, that a σ-compact non-locally compact topological group with a bc -base is zero-dimensional. Two more results in this paper are worth mentioning: 1) if the free topological group F(X)F(X) of a Tychonoff space X has a bc -base, then ind(X)≤0ind(X)≤0, and 2) a topological group G has a bc-base if and only if G can be compactified by a zero-dimensional remainder.
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- Special issue dedicated to the memory of Vitaly Vitalievich Fedorchuk
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