ON DIFFERENTIABLE MAPPINGS,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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This article contains mathematical proofs of three theorems on differentiable mappings. Theorems 1 and 2 establish the character of behavior of a mapping near an individual point at which the Jacobian is not equal to zero. Theorem 3 asserts that if the Jacobian is positive is negative at some point, then it is positive is negative also on a set of positive size, and the image of this set is also set of positive size.