Rational space
= Rational space
In the <simply connected> <homotopy category>, a <rational space> is a <simply connected> <CW complex> whose positive <homotopy groups> are <vector spaces> over $\mathbb Q$. Multiplication by every nonzero integer on these groups is invertible. More generally one uses nilpotent spaces with localized <fundamental group> and higher <homotopy groups>; the <simply connected> version avoids local-coefficient twisting.