second countable
A topological space
is said to be second if it has a countable basis (http://planetmath.org/BasisTopologicalSpace).It can be shown that a space is both Lindelöf and separable, although the converses fail. For instance, the lower limit topology on the real line is both Lindelöf and separable, but not second countable.
| Title | second countable |
| Canonical name | SecondCountable |
| Date of creation | 2013-03-22 12:05:06 |
| Last modified on | 2013-03-22 12:05:06 |
| Owner | rspuzio (6075) |
| Last modified by | rspuzio (6075) |
| Numerical id | 17 |
| Author | rspuzio (6075) |
| Entry type | Definition |
| Classification | msc 54D70 |
| Synonym | second axiom of countability |
| Synonym | completely separable |
| Synonym | perfectly separable |
| Synonym | second-countable |
| Related topic | Separable |
| Related topic | Lindelof |
| Related topic | EverySecondCountableSpaceIsSeparable |
| Related topic | LindelofTheorem |
| Related topic | UrysohnMetrizationTheorem |
| Related topic | FirstAxiomOfCountability |
| Related topic | LocallyCompactGroupoids |
| Related topic | FirstCountable |