first countable
Let be a topological space and let . is said to be at if there is a sequence of open sets such that whenever is an open set containing , there is such that .
The space is said to be if for every , is first countable at .
Remark. Equivalently, one can take each in the sequence to be open neighborhood of .
Title | first countable |
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Canonical name | FirstCountable |
Date of creation | 2013-03-22 12:23:33 |
Last modified on | 2013-03-22 12:23:33 |
Owner | Evandar (27) |
Last modified by | Evandar (27) |
Numerical id | 5 |
Author | Evandar (27) |
Entry type | Definition |
Classification | msc 54D99 |
Synonym | first axiom of countability |
Related topic | SecondCountable |
Related topic | TestingForContinuityViaNets |