[分析] open set ?

[iamagine (A-gine)]

Consider the space C([0,1]) = {f:[0,1] → |R | f is continous }

                                           1
and for f,g E C([0,1]) , define d(f,g) = ∫  |f(x)-g(x)|dx.
                                           0

Is the set {f E C([0,1]) : f(x) > 0 ,for all x E [0,1]} open in

the space (C([0,1]),d) ?


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※ 編輯: iamagine        來自: 120.107.174.106      (06/06 13:32)