No, there are points in A for which every neighbourhood of the point contains

points not in the set.

Yes, it contains all its limit pointsb) Is A closed?

(check these from here on)c) What is int A?

{(x,y): x^2+y^2<4, and y>x}

{(x,y): x^2+y^2>4, or y<x}d) What is ext A?

{(x,y): x^2+y^2=4, and y>x}U {(x,y): y=x and x in [-sqrt(2),sqrt(2)]} U {(2,2)}e) What is bd A?

yesf) Is A bounded?

It is closed and bounded and so compact.g) Is A a compact subset of R^2?

RonL