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In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain.
Also, "monsters" (nowhere continuous functions, continuous but nowhere differentiable functions, space-filling curves) began to be investigated.
As a consequence of the Stone-Weierstrass theorem, the graph of this operator is dense in XxY, so this provides a sort of maximally discontinuous linear map (confer nowhere continuous function).