1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Topology calculation help

  1. Mar 17, 2010 #1
    Let [itex]\mathbb{RP}^n= ( \mathbb{R}^{n+1} - \{ 0 \} ) / \sim[/itex] where [itex]x \sim y[/itex] if [itex]y=\lambda x, \lambda \neq 0 \in \mathbb{R}[/itex] adn the equivalence class of [itex]x[/itex] is denoted [itex][x][/itex].

    what is the necessary and sufficient condition on the linear map [itex]f : \mathbb{R}^{n+1} \rightarrow \mathbb{R}^{m+1}[/itex] for the formula [itex][f][x]=[f(x)][/itex] to define a map

    [itex][f] : \mathbb{RP}^n \rightarrow \mathbb{RP}^m ; [x] \mapsto [f(x)][/itex]

    not a scooby.
  2. jcsd
  3. Mar 17, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    Re: Topology

    Well, it has to respect your equivalence relation, right? Map lines through the origin into lines through the origin. How can a linear f not do that?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook