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Prove that function is homeomorphism.
Let $$ f: \prod\limits_{1}^{\infty} ( \{0,2 \}, \mathcal{T} _{\delta}) \to ([0,1], \mathcal{T}_{e}):\{n_i \} \mapsto \sum_{i=1}^{\infty} \frac{n_i}{3^i} $$ Prove that $f$ and $f^{-1}$ are continuous.