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...

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- April 9th 2007, 03:03 PMtttcomraderA compact set contains in an open set...
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... - April 10th 2007, 06:11 AMPlato
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.