$\mathrm{R}^n$ for non-integer values of $n$?

Question

If I have a set of all possible $x$ for $x \in \mathrm{R}^n$ for non-natural number $n$, what meaning would this have and how would it be used?

For instance, if I had $\mathrm{R}^{2.5}$, would this be a set of something between 2-coordinates and 3-coordinates? Would it be only positive? Etc.

Thanks! I apologize in advance if this does not make sense.