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- E2
[09T] Let \(I=\{ 0,2\} \) and \(X=I^ℕ\), consider the map \(F:X→ C\) given by
\[ F(x)=∑_{n=0}^∞ 3^{-n-1} x_ n~ . \]
Show that it is a bijection.
Let’s now equip \(X\) with the topology defined in [2F9]. . Show that \(F\) is a homeomorphism.
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