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Deleted Neighborhood


A deleted neighborhood, also called a punctured neighborhood, of a point x is a neighborhood of x with x itself removed. In a metric space, the deleted epsilon-neighborhood of x is

 {y:0<d(x,y)<epsilon}.

Deleted neighborhoods occur in the definition of a limit, where the value at the limiting point need not be specified.


See also

Ball, Limit, Neighborhood, Punctured Set

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References

Apostol, T. M. Mathematical Analysis. Reading, MA: Addison-Wesley, 1974.

Cite this as:

Weisstein, Eric W. "Deleted Neighborhood." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DeletedNeighborhood.html

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