※ 引述《PttFund (批踢踢基金只進不出)》之銘言：
: In a metric space (S,d), let A be non-empty subset of S. Define
: a function f_A(x): S→R by the formula
: f_A(x) = inf { d(x,y) : y in A } for each x in S.
: The value f_A(x) is called the distance from x to A.
: (a) Prove that f_A is uniformly continuous on S.
: (b) Prove cl(A) = { x in S : f_A(x) = 0 }, where cl(A) means
: the closure of A.
這一題應該出自於 Rudin, Principles of Mathematical Analysis.
證明的關鍵在
|f_A(x) - f_A(y)|≦d(x,y).
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