0
$\begingroup$

What is meant by the notation :

$y \in \partial B_\epsilon (x_o)$

Where B is a Ball centred at $x_0$ with radius $\epsilon$

$\endgroup$
  • 2
    $\begingroup$ It means that $y$ belong to the boundary of the ball centred at $x_0$ with radius $\epsilon$, i.e. to the sphere centred at $x_0$ with radius $\epsilon$. $\endgroup$ – Dario Jun 27 '14 at 13:40
3
$\begingroup$

When you are in a normed space, with norm $\|\cdot \|$, then $$\partial B_\epsilon(x_0)=:\{x: \|x-x_0\|=\epsilon\},$$ the boundary of $B_\epsilon(x_0)$. More generally the notation $\partial E$, with $E$ a set, denotes its boundary.

$\endgroup$
2
$\begingroup$

It is the boundary of the ball.

$\endgroup$

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.