Suppose \(G\) is a topological group and \(X\) is a topological space . A left action of \(G\) on \(X\) is called action by homeomorphisms if and only if for every \(g\in X\) the map \(x\mapsto g\cdot x\) is a homeomorphism .
Suppose \(G\) is a topological group and \(X\) is a topological space . A left action of \(G\) on \(X\) is called action by homeomorphisms if and only if for every \(g\in X\) the map \(x\mapsto g\cdot x\) is a homeomorphism .