Let $(M, \tau)$ a topological space, $N$ a smooth manifold and $f: M \to N$ a continuous map. If exists an maximal atlas on $M$ such that

Question

I'm trying to solve the following question:

Let $(M, \tau)$ a topological space, $N$ a smooth manifold and $f: M \to N$ a continuous map. If exists a maximal atlas $\mathcal{A}$ on $M$ such that $\tau=\tau_{\mathcal{A}}$ and $f$ is a smooth immersion, how I can prove that $\mathcal{A}$ is unique?