In mathematics, a function is locally bounded if it is bounded around every point. A family of functions is locally bounded if for any point in their domain all the functions are bounded around that point and by the same number.
== Locally bounded function ==
A real-valued or complex-valued function f defined on some topological space X is called locally bounded
if for any x0 in X there exists a neighborhood A of x0 such that
f (A) is a bounded set, that is, for some number M>0 one has
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