show that$ U=\{(x,y) \text{is an element of} \mathbb{R^2}:x^2+4y^2<4\}$ is open by finding a ball around each point which is contained in U I am trying to figure out how to do this one.I know that it is an open set but I don't know how to prove that it is open. I know how to show the ball around each point contained in U but not the overall graph of the ball and what I need to show that it is open.
For any point in U there is a minimum distance to the boundary of the ellipse which is > 0. Just make your neighborhood smaller than that value and it will be open.
For any point in U there is a minimum distance to the boundary of the ellipse which is > 0. Just make your neighborhood smaller than that value and it will be open.