1
$\begingroup$

What does the notation $p/|p|$ mean in topology? I guess it's associated with boundary/restriction of a map, but don't know how it is strictly defined...

$\endgroup$
  • 1
    $\begingroup$ What is $p$? In what context have you seen this notation? For me this could be a non-zero point $p$ in $\Bbb R^n$, divided by its norm $\|p\|$. $\endgroup$ – Watson Mar 25 '16 at 13:55
  • $\begingroup$ Guillemin Pollack , page 81. Here is a link: math.ucr.edu/~res/math260s10/old/difftopGP.pdf $\endgroup$ – futures Mar 25 '16 at 13:56
2
$\begingroup$

It just refers to the function $f(x)=p(x)/\|p(x)\|$, where the $\|\cdot \|$ term is the Euclidean norm, and $p$ has codomain $\Bbb R^n$. This is well defined and smooth if $p$ is never zero, and has image on the unit sphere.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.