Norm Topology

The norm topology on a normed space is the topology consisting of all sets which can be written as a (possibly empty) union of sets of the form

$B_r(x)={y in X:||y-x||_X<r}$

for some and some real number . Sets of the form are called the open balls in .

This entry contributed by Christopher Stover

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References

Rudin, W. Functional Analysis. New York: McGraw-Hill, 1991.

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Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "Norm Topology." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NormTopology.html

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