- #1
bobsmiters
- 12
- 0
I have no luck with proofs...
Prove that B[tex]_{r}[/tex] ((x[tex]_{0}[/tex], y[tex]_{0}[/tex])) = {(x,y) : || (x,y) - (x[tex]_{0}[/tex], y[tex]_{0}[/tex])|| < r} is an open set in R.
Now I know that to be an open set if and only if each of its points is an interior point and if it contains no boundary points. I would consider trying to prove it for any (a,b) [tex]\in[/tex] B[tex]_{r}[/tex]
Any ideas?
Prove that B[tex]_{r}[/tex] ((x[tex]_{0}[/tex], y[tex]_{0}[/tex])) = {(x,y) : || (x,y) - (x[tex]_{0}[/tex], y[tex]_{0}[/tex])|| < r} is an open set in R.
Now I know that to be an open set if and only if each of its points is an interior point and if it contains no boundary points. I would consider trying to prove it for any (a,b) [tex]\in[/tex] B[tex]_{r}[/tex]
Any ideas?