Hi(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Algebric geometry

Loading...

Similar Threads for Algebric geometry | Date |
---|---|

I Diffeomorphism invariance and contracted Bianchi identity | Apr 13, 2018 |

A Smoothness of multivariable function | Apr 10, 2018 |

A Smooth extension on manifolds | Apr 5, 2018 |

I Manifold with a boundary | Apr 4, 2018 |

**Physics Forums - The Fusion of Science and Community**