General topology Metric spaces Concept
Totally bounded set
Summary
A subset of a metric space is totally bounded when, for each size, it can be covered by finitely many pieces of that size. Compact sets are exactly the totally bounded sets that are complete.
Where this leads
2 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Totally_bounded_space, lead section
About this page
| Tag | 020Q06TYYH |
|---|---|
| URI | m2://020Q06TYYH |
| Aliases | totally-bounded-space, precompact-set |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54E35 |
| Specializes | Bounded set |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.