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
 |
for some 
and for some number 
.
Sets of the form 
are called the open balls in 
.
Norm Topology
This entry contributed by Christopher Stover
Explore with Wolfram|Alpha
References
Rudin, W. Functional Analysis. New York: McGraw-Hill, 1991.Cite this as:
Stover, Christopher. "Norm Topology." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/NormTopology.html