Topology of pointwise convergence

This article defines a function space topology i.e. a topology on the collection of continuous maps between two topological spaces

Definition

Suppose $X$ and $Y$ are topological spaces. Let $C(X,Y)$ denote the space of continuous maps from $X$ to $Y$. The topology of pointwise convergence on $C(X,Y)$ is a topology such that convergence of a sequence of elements in the topology is equivalent to their pointwise convergence as functions.

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