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gptkbp:instanceOf
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gptkb:mathematical_concept
Kähler manifold
one-dimensional complex projective space
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gptkbp:alsoKnownAs
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extended complex plane
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gptkbp:automorphismGroup
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gptkb:Möbius_transformations
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gptkbp:category
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gptkb:Riemannian_manifold
surface
projective variety
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gptkbp:compact
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true
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gptkbp:compactificationOf
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gptkb:complex_plane
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gptkbp:contains
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complex numbers
point at infinity
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gptkbp:dimensions
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1
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gptkbp:fieldOfStudy
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gptkb:algebraic_geometry
gptkb:geometry
gptkb:mathematics
gptkb:topology
complex analysis
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gptkbp:genus
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0
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gptkbp:hasChart
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gptkb:stereographic_projection
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gptkbp:hasModel
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projective line over complex numbers
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gptkbp:hasPoint
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one
zero
infinity
arbitrary complex number
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https://www.w3.org/2000/01/rdf-schema#label
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Riemann sphere
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gptkbp:isomorphicTo
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gptkb:2-sphere_(S^2)
gptkb:CP^1
complex projective line
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gptkbp:namedAfter
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gptkb:Bernhard_Riemann
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gptkbp:relatedTo
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gptkb:Möbius_group
gptkb:stereographic_projection
conformal mapping
meromorphic functions
complex projective geometry
extended complex plane
fractional linear transformations
rational functions
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gptkbp:simplyConnected
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true
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gptkbp:structure
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complex structure
differentiable structure
projective structure
topological structure
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gptkbp:symbol
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ℂ̂
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gptkbp:topology
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homeomorphic to the 2-sphere
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gptkbp:usedIn
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gptkb:geometry
gptkb:stereographic_projection
complex analysis
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gptkbp:bfsParent
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gptkb:Riemannian_manifold
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gptkbp:bfsLayer
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5
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