- #1
- 4,807
- 32
Hello all,
I am reading an article and there is something I find odd. The setting is a Banach space E and we have two disjoint closed subsets A and B of E. There is no additional assumption on E, A or B. The author then says,
"Let f:E-->[0,1] be a Urysohn's function such that f(x)=0 if and only if x is in A, and f(x)=1 on B."
But never have I seen a version of Urysohn's lemma that guarantees that f(x)=0 if and only if x is in A.
Does someone have an explanation? (I would ask my advisor but she had gone on vacation for 3 weeks)
I am reading an article and there is something I find odd. The setting is a Banach space E and we have two disjoint closed subsets A and B of E. There is no additional assumption on E, A or B. The author then says,
"Let f:E-->[0,1] be a Urysohn's function such that f(x)=0 if and only if x is in A, and f(x)=1 on B."
But never have I seen a version of Urysohn's lemma that guarantees that f(x)=0 if and only if x is in A.
Does someone have an explanation? (I would ask my advisor but she had gone on vacation for 3 weeks)