What is $\chi _{[-.5,.5]} (x)$ notation in textbook?

Question

I'm reading Introduction to Wavelets by David Walnut. In the book, he uses a notation $\chi_{interval}(x)$, not sure what it is. He does produce graphs of these, here are examples

$\chi_{[-.5,.5]} (x)$ is a square impulse/ top-hat function with constant height 1 over interval.

$\chi _{[0,\pi]} (x)$ is a linear line, starting from $y = 0$ at $x = 0$ to $y = \pi$ at $x = \pi$

Answer 1

It is an indicator function; a piecewise function that equals one whenever the argument falls within the indicated interval, but equals zero otherwise.$$\raise{0.5ex}\chi_{[-0.5;0.5]}(x)~=~\begin{cases}1 &:& -0.5\leqslant x\leqslant 0.5\\0&:&\text{otherwise}\end{cases}$$

---

$\chi _{[0,\pi]} (x)$ is a linear line, starting from $y = 0$ at $x = 0$ to $y = \pi$ at $x = \pi$

This would be an error.$$y~=~\raise{0.5ex}\chi_{[0;\pi]}(x)~=~\begin{cases}1 &:& 0\leqslant x\leqslant \pi\\0&:&\text{otherwise}\end{cases}$$