I'm just hoping that someone can verify what i write next,
the set }
is closed because the epsilon-neighbourhood around the lower limit, 0, will intersect elements in R-positive
is that adequate reasoning?
is closed if and only if contains all its adherent points. is an adherent point of if for every radius , the ball , that is, { } has a non-empty intersection with . Is 0 an adherent point and does contains 0?
I'm just hoping that someone can verify what i write next,
the set }
is closed because the epsilon-neighbourhood around the lower limit, 0, will intersect elements in R-positive
is that adequate reasoning?
Originally Posted by bram kierkels
is closed if and only if contains all its adherent points. is an adherent point of if for every radius , the ball , that is, { } has a non-empty intersection with . Is 0 an adherent point and does contains 0?
Well, I guess that it depends on what topology has. If it's the usual topology then the above user has the correct reasoning.