c[0,1] represents the set of continuous functions on [0,1] d(f,g)= sqrt( integral( |f-g|^2, from 0 to 1)) is (c,d) complete? any counterexample if not?
Follow Math Help Forum on Facebook and Google+
Consider this sequence: $\displaystyle f_n (x) = \left\{ {\begin{array}{lr} {nx} & {0 \leqslant x \leqslant \frac{1}{n}} \\ 1 & {\frac{1}{n} < x \leqslant 1} \\ \end{array} } \right.$
View Tag Cloud