second countable

A topological spaceMathworldPlanetmath is said to be second if it has a countable basis ( 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