Let us define $\mathbb{P}=\mathbb{R}\backslash\mathbb{Q}$. Find all path-connected components of $\mathbb{P}^n\cup\mathbb{Q}^n$
I tried solving this question but I'm out of luck. Any help, please?
It is not a duplicate of Connectedness of points with both rational or irrational coordinates in the plane? because they prove connectivity of the set and not path-connectivity.
In the paragraph above there is an explanation of why this is NOT a duplicate of an existing post, please look closely at the questions asked...