Which of the following are manifolds :
1) a sphere
2) a cone
3) an ellipse
4) a pair of intersecting planes
and which of the above are differential manifolds and why?
I don't think (d) means the intersection of a pair of intersecting planes (which would be either a line or a plane, hence a manifold), but rather means the union of two planes that happen to intersect (which will not be a manifold - unless the planes are the same).