Choose a point
Then the maximum such that is:
.
But, if you want to show the given square is open, you need to show that for all
Given the set S={(x,y): |x|<1 , |y|<1} prove that is open in .
Using the definition of the open set we have:
S is open in iff for all ,there exists an ε>0 such that ,for all :
.
.......................................OR......... ..................................................
if ,there exists an ε>0 such that:
What is the epsilon ,so that the implication can be satisfied ??
That is as far i can go.
Any suggestions??