Definition 3.4.4 (Inverse images). If \(U\) is a subset of \(Y\), we define the set \(f^{-1}(U)\) to be the set $$ f^{-1}(U):=\{x\in X: f(x)\in U\} $$ In other words, \(f^{-1}(U)\) consists of all the elements of \(X\) which map into \(U\): $$ f(x)\in U\iff x\in f^{-1}(U) $$ We call \(f^{-1}(U)\) the inverse image of U.
Definition 3.4.4
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Exercise 3.4.2
\(\equiv\) { Definition 3.4.4 }
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Exercise 3.4.1
\(=\) { Definition 3.4.4 }