Question

Show that A={(x,y)R^2/ 1 13 years ago

Answer 1

Take a=(x,y) in A. Let
\[ c =\sqrt{x^2+y^2} \\
r=\frac 1 2 Minimum\{ c-1, 7-c\}
\]
The disk of center a and radius r is contained in A.
We showed that every element in a belongs to disk that is contained in A. So A is open.