General topology Separation axioms Concept
Separation axioms
Summary
The separation axioms are conditions on a topological space that say how well open sets can separate points and closed sets. The main ones, from weak to strong, are T0, T1, Hausdorff, regular and normal.
Remarks
Each of these axioms, together with T1, implies the axioms before it in this list. Each metric space satisfies all of them, by metric spaces are Hausdorff and metrizable spaces are normal. Authors do not agree on all names. For example, some authors include T1 in the definition of a regular or normal space, and some do not.
Further reading
- Web https://en.wikipedia.org/wiki/Separation_axiom, lead section
- Web https://en.wikipedia.org/wiki/Separation_axiom, Main definitions
About this page
| Tag | 04J4BYB0XE |
|---|---|
| URI | m2://04J4BYB0XE |
| Aliases | tychonoff-separation-axioms |
| Kind | concept |
| Writing | W1 stated |
| MSC | 54D10 |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W2
- edge defines in: at least one definition (0 of 1)
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
No page links to this page yet.