Problem: Let K be a compact subset in R^n. Suppose O is an open subset of R^n that contains K, prove there exists a postive number r such that Nr(u) equals to O for every u in K.
My proof:
.......
I don't even know how to start...
Problem: Let K be a compact subset in R^n. Suppose O is an open subset of R^n that contains K, prove there exists a postive number r such that Nr(u) equals to O for every u in K.
My proof:
.......
I don't even know how to start...
Does the notation Nr(u) stand for a ball centered at u with radius r?
If it does, and “Nr(u) equals to O for every u in K” is correctly written then the statement is false. However, if it reads “Nr(u) is a subset of O for every u in K” then that can be proved
Please review and advise. Tell we us about the definitions.