Does there exists an infinite subset $S$ of $C([0,1],\mathbb{R})$ such that $$\int_0^1|f(x)-g(x)|dx=1$$ for any distinct $f,g\in S$?
I was guessing the the answer is yes. I can construct such a set with 3 functions, but can't really be generalized.
Does there exists an infinite subset $S$ of $C([0,1],\mathbb{R})$ such that $$\int_0^1|f(x)-g(x)|dx=1$$ for any distinct $f,g\in S$?
I was guessing the the answer is yes. I can construct such a set with 3 functions, but can't really be generalized.