Frölicher space

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. A map

is called smooth if for each smooth curve c in C_A, m.c is in C_B. Furthermore, the space of all such smooth maps has itself the structure of a Frölicher space. The smooth functions on

are the images of

...
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