Quote: define the inverse of a function f by its properties on subsets of f's range

Note

let f:X->Y be an arbitrary mapping with B as a subset of Y. Then the properties of the inverse of f "are satisfyingly complete, and can be stated as follows: [g = inverse of f] g(empty set) = empty set; g(Y)=X; B1 a subset of B2 implies g(B1) subset g(B2); g(union Bi) = union (g (Bi)); g(intersection Bi) = intersection (g (Bi)); g( complement B) = complement (g(B)).

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Topic: topology (29 items)