Example · High school
Terms
| Term | This example | Why |
|---|
| interior |
$\operatorname{int} [0, 1) = (0, 1)$
|
The interior of $[0, 1)$ is $(0, 1)$, because every point of $(0, 1)$ has a small interval around it within $[0, 1)$.
|
| boundary |
$\partial [0, 1) = \setdef{0, 1}$
|
The boundary contains $1$ even though the set does not, and $0$ even though the set does.
|
| exterior |
$\operatorname{ext} [0, 1) = (-\infty, 0) \cup (1, \infty)$
|
|
| closure |
$\overline{[0, 1)} = [0, 1]$
|
The closure of $[0, 1)$ adds the missing boundary point $1$.
|
| open set |
✗ |
The interval $[0, 1)$ is not open in $\reals$, because every interval around $0$ contains negative numbers.
|
| closed set |
✗ |
The interval $[0, 1)$ is not closed in $\reals$, because it does not contain its boundary point $1$.
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