Because all points on D have points on D in any centripetal neighborhood, there are no isolated points.

In fact, all the points on d are the gathering points of d.

It is neither an open set nor a closed set, but a semi-open and semi-closed set.

It's not a region. The region requires all points to be interior points, but the points on x 2+y 2 =1are not interior points, but boundary points.