on $\displaystyle R^2$ we define an order topology (lexicographic order) as follow: $\displaystyle (x1,y1)>(x2,y2)$ if $\displaystyle x1>x2$ or ($\displaystyle x1=x2$ & $\displaystyle y1>y2$).

Is this topology equivalent to the standard topology? if not, which topology is finer?(give an example of an open set in one but not in the other)?

thanks :)