As you can see in the picture, it may happen that the intersection consists of more than one connected component. In our example this happens because the outline of curves around and re-enters the disc again at a place away from However, that’s only because we chose to be quite large. By making smaller we can ensure that the intersection of and consists of only one connected component. A shape (drawn in the plane) is locally connected at if the intersection of a disc centred at and consists of a single connected component for all discs whose radii are small enough.