- #1
patricia-donn
- 5
- 0
Hello
Would anyone out there be able to help me with a problem I'm having? I have to prove that a function is open and that another is closed. The question is:
Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x²+2
Let A={g Є C[0,1]: d(g,f) > 3}. Prove that A is an open set
Let B={g Є C[0,1]: 1 ≤ d(g,f) ≤ 3}. Prove that B is a closed set
I'm new to all of this and just don't know what to do even with the f(x)=x²+2 part so if anyone out there can shed some light, I'd be really grateful!
Thanks
Would anyone out there be able to help me with a problem I'm having? I have to prove that a function is open and that another is closed. The question is:
Consider C [0,1] with the sup metric. Let f:[0,1]→R be the function given by f(x)=x²+2
Let A={g Є C[0,1]: d(g,f) > 3}. Prove that A is an open set
Let B={g Є C[0,1]: 1 ≤ d(g,f) ≤ 3}. Prove that B is a closed set
I'm new to all of this and just don't know what to do even with the f(x)=x²+2 part so if anyone out there can shed some light, I'd be really grateful!
Thanks