Sentence:  Every circle \gamma on the <WSD>Riemann sphere</WSD> \Sigma which does not go through a given point P^\in\Sigma divides \Sigma into two parts, such that one part contains P^ and the other does not. 
Meaning of the word marked with <WSD> tags:  The 2-sphere embedded in Euclidean three-dimensional space and often represented as a unit sphere, regarded as a homeomorphic representation of the extended complex plane and thus the extended complex numbers.