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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.

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    @voldemort: Kindly avoid posting same question more than once and a homeomorphism by definition is bicontinuous.2012-11-04
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    Ok. From this time I will respect this rules. I'm new here so i hope that you will forgive me :) My problem is that I don't know how to prove that this is homeomorphism :(2012-11-04
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    @Marvis: This wouldn’t have happened if I’d been quicker responding to voldemort’s request for more help on the original question. At this point I think that it makes better sense to leave this question open, since the more extensive answer is here; there are two pointers to the earlier question that allow access to anything there that isn’t here.2012-11-04
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    @BrianM.Scott, you don't have to be quicker! You're helping me and I'm not allowed to demand from you anything. I can just be greatfull that you want to help me :)2012-11-04

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