A) Show that the union of two nonempty open sets is open.

I have this theorem to use: A set D is open iff it contains no point of its boundary.

Can someone show have to give a solid proof of A...

Thanks in advance for any help

Printable View

- Feb 1st 2010, 09:28 PMjzelltOpen sets Proof
A) Show that the union of two nonempty open sets is open.

I have this theorem to use: A set D is open iff it contains no point of its boundary.

Can someone show have to give a solid proof of A...

Thanks in advance for any help - Feb 2nd 2010, 11:08 AMtttcomrader
Here is what I think:

Say I have open sets X and Y, then for , I can find an open ball centered at them such that the entire ball is in X and Y, respectively.

Well, then, if you pick any point in , that that point is either in X or Y, well, then, you can draw another open ball that is contained in either X or Y.

So if you use radius for the points in X and Y, you can just use radius

Hope this helps. - Feb 2nd 2010, 12:11 PMDrexel28