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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?

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  • $\begingroup$ Does your space have a suitable convexity structure? $\endgroup$ Aug 23, 2019 at 18:49
  • $\begingroup$ No, but why would that matter, since the homeomorphism I'm looking for need not be linear. $\endgroup$
    – ABIM
    Aug 26, 2019 at 16:54
  • $\begingroup$ Simple for spaces with additional (convex or group) structure there are many results establishing their topological equivalence to Frechet spaces. $\endgroup$ Aug 27, 2019 at 14:31

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