Example · High school
Terms
| Term | This example | Why |
|---|
| paracompact |
✓ |
$\mathbb{Q}$ is paracompact because it is a metric space.
|
| measure zero |
✓ |
$\mathbb{Q}$ has measure zero, because it is countable.
|
| dense set |
✓ |
|
| countable |
✓ |
|
| meager set |
✓ |
$\mathbb{Q}$ is meager, because it is a countable union of single points, and each point is nowhere dense in $\reals$.
|
| compact |
✗ |
|
| sequentially compact |
✗ |
The set of rational numbers, $\mathbb{Q}$, is not locally compact, because no neighborhood of a point has a compact closure, so it is not compact or sequentially compact either.
|
| locally compact |
✗ |
|
| nowhere dense |
✗ |
$\mathbb{Q}$ is not nowhere dense, because it is dense in $\reals$.
|
| uncountable |
✗ |
|
Distinctions using this example
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