On extending the action (Q1803039)

The author proves that the problem of extending the action of a bicompact zero-dimensional group is solvable, i.e., for a given bicompact zero- dimensional group \(G\) acting on the metric \(G\)-space \({\mathcal X}\) of the associated orbit space \(X\), and for any closed inclusion \(i: X\to Y\) into the metric space \(Y\), there exists a \(G\)-space \({\mathcal Z}\) which extends the action of \(G\) on \({\mathcal X}\) parallel to the inclusion \(i\).