Talk:Real projective space

Equivalence class
could the equivalence class be written like this: [v] = \{ \lambda v: v \epsilon R^{n+1} -{0} \and \lambda \epsilon R^* \}


 * You wouldn't put the constraints on v inside the set braces, since v doesn't vary. So you'd write: "the equivalence class of v \epsilon R^{n+1}-{0} is [v] = \{ \lambda v: \lambda \epsilon R^* \}". AxelBoldt 21:22, 19 Nov 2004 (UTC)

Could we put some more properties about RP$n$ in? Such as the Euler characteristic and homology groups?

Orientability
Which projective spaces are non-orientable? A5 02:11, 26 May 2006 (UTC)


 * RPn for n even. -- Fropuff 03:52, 26 May 2006 (UTC)

homology and orientability
You cannot use homology theory to prove that real projective space is orientable for n odd. The theorem is that if a compact manifold is orientable, then its top de rham cohomology group is nonzero. By a sketchy argument of sorts, you can use the contrapositive to show that it is not orientable for n even. But, then you need de Rham's theorem, universal coefficients theorem, and the fact that Q is an injective object in the abelian category of Z-modules. I'm highly distrusting of the second proof give too. The fact is you need to consider the pushforward of the continuously oriented local frames on the sphere. The proof is not short nor is it trivial. —Preceding unsigned comment added by Agapendures (talk • contribs) 04:10, 19 August 2009 (UTC)

Maths in LaTeX
Please, try to write all the maths formulae in La Te X, not in bold letters.--JBecerra (talk) 12:06, 27 January 2017 (UTC)

It seems a bit odd to omit mention of the double cover S1 → RP1
In the section Low-dimensional examples there is a nice mention of the covering map S3 → RP3, and the fact that these are Lie groups. So it seems a bit odd to omit mention of the even simpler double cover S1 → RP1. (And why not also mention the n-fold covers S1 → RP1 and their (its) Lie group status as well?)50.205.142.35 (talk) 20:12, 23 February 2020 (UTC)