Assertion: möbius transformation | /r/HasProperty | bijective conformal maps
Facets:
value: from the riemann sphere
type: LOCATION
value: to the riemann sphere
type: TRANSITIVE-OBJECT
value: always
type: DEGREE
value: exactly
type: DEGREE
Source sentences:
text: The Möbius transformations are exactly the bijective conformal maps from the Riemann sphere to itself, i.e., the automorphisms of the Riemann sphere as a complex manifold; alternatively, they are the automorphisms of C P 1 {\displaystyle \mathbf {C} \mathbf {P} ^{1}} as an algebraic variety.
text: Thus a Möbius transformation is always a bijective holomorphic function from the Riemann sphere to the Riemann sphere.