General topology Basic notions: open sets, neighbourhoods, bases Concept
Subbasis
Summary
A subbasis of a topology is a family of open sets that generates the topology. The topology is the smallest one in which all members of the family are open. The finite intersections of members of a subbasis form a basis.
Where this leads
7 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Subbase, lead section
About this page
| Tag | 09S8DV34Y0 |
|---|---|
| URI | m2://09S8DV34Y0 |
| Aliases | subbase, prebase |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54A05 |
| 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.
What links here
Definitions
Special cases
Used by
- Vietoris topology
- Topology of pointwise convergence
- Order topology
- Initial topology
- Alexander subbase theorem
- Lawson topology
- Compact-open topology