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Local Base


Let X be a topological vector space and for an arbitrary point x in X, denote by N_(x) the collection of all neighborhoods of x in X. A local base at x is any set B subset N_(x) for which each element U in N_(x) includes some member of B.

A local base at a point x is sometimes called a local base of neighborhoods at that point.


This entry contributed by Christopher Stover

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References

Wilansky, A. Modern Methods in Topological Vector Spaces. New York: Dover, 2013.

Cite this as:

Stover, Christopher. "Local Base." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LocalBase.html

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