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This is just to recall a nice fact:
Any two points ##A,B\in\mathbb{R}^n\backslash\mathbb{Q}^n,\quad n>1## can be connected with a ##C^\infty##-smooth curve that does not intersect ##\mathbb{Q}^n##.
The proof is surprisingly simple: see the attachment
Any two points ##A,B\in\mathbb{R}^n\backslash\mathbb{Q}^n,\quad n>1## can be connected with a ##C^\infty##-smooth curve that does not intersect ##\mathbb{Q}^n##.
The proof is surprisingly simple: see the attachment