One theorem partly named for this operation is used to prove the submersion theorem by showing that under a smooth map, the preimage of a regular value is a manifold. A theorem partly named for this operation can be proved by showing the sum of the identity map and a certain Lipschitz map is a bi-Lipschitz homeomorphism, implied by the contraction mapping theorem. Unlike the standard form of another type of this operation, a form named for Moore and Penrose is not (*) continuous. (-5[1])Right multiplication by this operation on a group element gives a group action. Groups are monoids where this operation can be applied (10[1])to every element. A map is bijective if and only if it has one of these (10[1])things. It’s not reciprocal, but a superscript of minus one denotes this type of function. (10[1])For 10 points, give this word denoting a function that “undoes” the original function. ■END■