In mathematics, Frölicher spaces extend the notions of calculus and smooth manifolds.
They were introduced in 1982 by the mathematician Alfred Frölicher.
A Frölicher space consists of a non-empty set X together with a subset C of Hom(R, X) called the set of smooth curves, and a subset F of Hom(X, R) called the set of smooth real functions, such that for each real function in F and each curve in C, the following axioms are satisfied: Let A and B be two Frölicher spaces.
The smooth functions on are the images of
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