Continuous function in microeconomics In the following picture two preference relations are defined - 

Ist preference relation defines lexicographic relation. Though we know that lexicographic preferences doesn't have utility function. They are defined at a point so we cannot define a utility function - is discontinuous. But how can we show it in terms of upper and lower contour set being closed?

Why second one is continuous? 

Note - some terminologies - 

A binary relation >~ on the metric space X is continuous if, for all x in X, the upper and lower contour sets, { y in X : y > ~ x} and {y in X : x >~ y}, respectively, are closed. 

The upper contour set of x is >~ (x) = {y in X : y >~ x} 

The lower contour set of x is >~ (x) = {y in X : x>~ y}
Take $y_1=y_2=1$. As the figure below shows, the lower left segment of the boundary of the upper contour set of the lexicographic preference is open.