is the set A={ (x,y)∈R² : x²+ y² =1} connected? how do we prove it?
is there any general proof? or some quick method by which we can tell any set is connected or not
If f : [0,1] -> R2 defined by f(t) = (cost, sint) then the map is continuous and the closed interval [0,1] is connected. So the image of f should be connected.and i think the image of f is exactly the unit circle centerd at origin. is it right?
but is there any general method for proving or disproving any subset of R2 connected?