[其他] 為何很多數學定義都用preimage來做？
好像有不少定義是用反過來定的，也就是使用preimage
如：
continuous function f: for every open set A, f^(-1)(A) is open.
measurable function f: for every measurable set A, f^(-1)(A) is measurable.
measure-preserving function f: m(A) = m(f^(-1)(A))
為何不用f(A)？這樣不是比較自然嗎？
跟函數map的方向相同。
請問大家對這個問題有何看法？謝謝。
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