::Neighbourhood (mathematics)


Point::topology    Number::called    Subset::space    Points::right    System::uniform    Thumb::first


A set <math>V</math> in the plane is a neighbourhood of a point <math>p</math> if a small disk around <math>p</math> is contained in <math>V</math>.
A rectangle is not a neighbourhood of any of its corners.

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. Intuitively speaking, a neighbourhood of a point is a set containing the point where one can move that point some amount without leaving the set.

This concept is closely related to the concepts of open set and interior.

Neighbourhood (mathematics) sections
Intro   Definition    In a metric space    Examples    Topology from neighbourhoods    Uniform neighbourhoods   Deleted neighbourhood  See also  References  

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