Exponential topologies
Given two topological spaces X and Y, you can consider the set Top(X,Y) of continuous functions from X to Y. You might like to put a topology on Top(X,Y) making it a topological space, not just a set. Exponential topologies are particularly nice topologies on the set Top(X,Y). In this video, I talk about exponential topologies and prove that when they exist, they are unique.
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