On a problem of Zambakhidze-Smirnov

Abstract

We say that the action extension problem is solvable for a bicompact groupG if for any metricG-space$\mathbb{X}$ and for any topological embeddingc of the orbit spaceX into a metric spaceY there exist aG-space ℤ, an invariant topological embeddingb:$\mathbb{X}$ → ℤ, and a homeomorphismh: Y → Z such that the diagram

is commutative. We prove the following theorem: for a bicompact zero-dimensional groupG, the action extension problem is solvable for the class of dense topological embeddings.