General topology Countability axioms Concept
First-countable space
Summary
A topological space is first-countable when each point has a countable family of neighbourhoods that controls all neighbourhoods of the point. In such spaces, sequences are enough to describe closures and continuity.
Where this leads
8 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/First-countable_space, lead section
About this page
| Tag | 0CP5NDD21C |
|---|---|
| URI | m2://0CP5NDD21C |
| Aliases | first-axiom-of-countability |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54D70 |
| Specializes | Topological space |
| 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)
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