- #1
Feynman
- 159
- 0
Hi
we define the projectif space [tex]P^n \mathbb{R}[/tex]
by the quotient space :[tex]\mathbb{R}^{n+1}/\sim[/tex] where:
[tex]x\sim y\Leftrightarrow x[/tex] et[tex]y[/tex] are colinaires.
my questions are :
1. How we proof that the restiction de [tex]\sim[/tex] on [tex]S^n[/tex] (where S^n is the sphere on n dimension) identify x and -x?
2. How this projectif reel space is homeomorphe to the quotient of S^n by this identification?
3.How we proof that [tex]P^{n}\mathbb{R}[\tex] is compact?
thanks
we define the projectif space [tex]P^n \mathbb{R}[/tex]
by the quotient space :[tex]\mathbb{R}^{n+1}/\sim[/tex] where:
[tex]x\sim y\Leftrightarrow x[/tex] et[tex]y[/tex] are colinaires.
my questions are :
1. How we proof that the restiction de [tex]\sim[/tex] on [tex]S^n[/tex] (where S^n is the sphere on n dimension) identify x and -x?
2. How this projectif reel space is homeomorphe to the quotient of S^n by this identification?
3.How we proof that [tex]P^{n}\mathbb{R}[\tex] is compact?
thanks