- #1

jlemus85

- 6

- 0

## Homework Statement

Show that the subset of E^2 given by { (x1,x2) belonging to E^2 : x1>x2} is open.

## Homework Equations

d(x,y)= sqrt[ (x1-y1)^2 +(x2-y2)^2 ]

## The Attempt at a Solution

Ok so I would like someone to tell me if I'm on the right track or if I'm way off.

So to show that a subset is open I need to show that if I choose an arbritrary point in my subset S, that I can form a ball around this point p and all the points near p will be within S.

So what I want to do is first draw a ball with center x and radius r. Then I want to draw another ball that is within the first ball with center y and radius r-d(x,y). If this set is open then y and the radius r-d(x,y) will belong to S.

SO far this is about as far as I can get without confusing myself and probably making you guys cringe me plugging in the distance formula and all that.

Any help would be very appreciated.