Inverse mapping theorem and local forms of continuous mappings (Q897972)

The authors prove the following inverse mapping theorem (without any differentiability assumptions): Let \(f:X\to Y\) be an open discrete continuous mapping between two oriented topological manifolds of the same dimension and assume that \(|\text{deg}(f,x_0)|=1\) for some \(x_0\in X\). Then \(f\) is a local homeomorphism at \(x_0\).