- \_^\infty

- f_n:X \longrightarrow Y

- \lim_ f_n(x) = f(x).

In mathematics, the qualifier
pointwise is used to indicate that a certain property is defined by
considering each value f(x) of some function f. An example is
pointwise
convergence of functions — a sequence of functions

- \_^\infty

- f_n:X \longrightarrow Y

- \lim_ f_n(x) = f(x).

An important class of pointwise concepts are the
pointwise operations — operations defined on functions by
applying the operations to function values separately for each
point in the domain
of definition. These include

Pointwise operations inherit such properties as
associativity,
commutativity and
distributivity
from corresponding operations on the codomain.

An example of an operation on functions which is
not pointwise is convolution.

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