ScalingStacks

Remark 7.3.7. Assume $X\subset{\mathbf{R}}^{N}$ is obtained by the construction of Remark 7.2.5. A homotopy class of paths in $X$ is smooth if and only if it contains a path $\gamma$ such that the composition $[0,1]\xrightarrow{\gamma}X\hookrightarrow{\mathbf{R}}^{N}$ is a smooth immersion.