Fix some point p on the Riemann sphere. Each Jordan curve not passing through p divides the Riemann sphere into two pieces, and we call the piece containing p the "exterior" of the curve, and the other piece its "interior".
Fix a point p on the Riemann sphere. Each Jordan curve not passing through p divides the Riemann sphere into two pieces, and we call the piece containing p the "exterior" of the curve, and the other piece its "interior".