Timeline for On the homotopy type of $\mathbb{QP}^\infty$

6 events

when toggle format	what		by	license	comment
Dec 22, 2017 at 22:31	comment	added	Eric Wofsey		That square certainly commutes. Maybe your question is whether the bottom map is an inclusion of a subspace? I believe the answer is yes again, but it takes a bit of work to prove--I don't think it follows automatically from density or anything like that. (Note, though, that the space $\mathbb{RP}^\infty$ here is not the space that is normally called $\mathbb{RP}^\infty$: the usual $\mathbb{RP}^\infty$ comes from giving a colimit topology to $\mathbb{R}^\infty$, not the product topology.)
Dec 22, 2017 at 21:41	comment	added	fosco		Is it true that the square $$ \begin{array}{ccc} \mathbb Q^\infty &\to &\mathbb R^\infty\\ \downarrow && \downarrow \\ \mathbb{QP}^\infty &\to &\mathbb{RP}^\infty\\ \end{array} $$ commutes? In principle, the quotient by multiplication for a nonzero rational gives a different quotient than multiplication for a nonzero real number; but I think the quotients are the same by density.
Dec 22, 2017 at 21:22	vote	accept	fosco
Dec 22, 2017 at 21:17	comment	added	fosco		This is the good answer I was hoping for
Dec 22, 2017 at 21:17	history	edited	Eric Wofsey	CC BY-SA 3.0	added 198 characters in body
Dec 22, 2017 at 21:12	history	answered	Eric Wofsey	CC BY-SA 3.0