Topology of function spaces

vector space equipped with a compatible topology

set of functions of a given kind from a set X to a set Y; it is called a space because in many applications it is a topological space (including metric spaces), a vector space, or both

mode of convergence of a function sequence

part of the domain of a mathematical function

notion of convergence in mathematics

theorem

a topology defined on the set of continuous maps between two topological spaces

topology of topological vector spaces

Topologies on the set of operators on a Hilbert space

collection of continuous functions

weak topology on function spaces

type of mathematical convergence in topology