※ 引述《TaiwanBank (澳仔金控台灣分行)》之銘言：
: Suppose that f: (-5,5) → R is a continuous function. Which
: of the following statements must be true and which could be
: false? (Give reasons for your answers)
: (a) The set { f(x) : 0 < x < 1 } is open.
: (b) The set { f(x) : 0 < x < 1 } is bounded.
: (c) f is uniformly continuous on the interval (-1,1).
(a) False, suppose f(x)=0 => the set { f(x) : 0 < x < 1 } = {0} is closed
(b) 連續函數保持緊緻性 => the set { f(x) : 0 ≦ x ≦ 1 } is compact
這導致 { f(x) : 0 < x < 1 } 有界
(c) 連續函數 f 在緊緻集 [1,-1] 上是均勻連續
由定義可推得在 (-1,1) 上亦均勻連續
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