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I am studying rough paths from the 2007 St Flour lecture notes and I came across the example at the end of chapter one of the sequence of paths $X(n):[0,2\pi]\to \mathbb R^2$ given by $X_t(n) = \frac{...

Let $\Omega G^p([0,T];\mathbb{R}^n)$ be a space of $p$-geometric rough paths with values in $\mathbb{R}^n$. Is $\Omega G^p([0,T];\mathbb{R}^n)$ homeomorphic to some Fr\'{e}chet space?