The Real Projective Plane

URI: https://gptkb.org/entity/The_Real_Projective_Plane
GPTKB entity
Statements (32)
Predicate Object
gptkbp:instanceOf gptkb:geometry
surface
non-orientable surface
closed surface
2-manifold
compact surface
gptkbp:canBe attaching a disk to a Möbius strip
gptkbp:canBeImmersedIn gptkb:3-dimensional_Euclidean_space
gptkbp:cannotBeEmbeddedIn gptkb:3-dimensional_Euclidean_space
gptkbp:containsGenus 0
gptkbp:Euler_characteristic 1
gptkbp:fundamentalGroup cyclic group of order 2
gptkbp:hasHomologyGroup H_1 = Z/2Z
H_2 = 0
https://www.w3.org/2000/01/rdf-schema#label The Real Projective Plane
gptkbp:isDualTo gptkb:the_Fano_plane
gptkbp:isNamedAs gptkb:real_projective_plane
gptkb:RP^2
gptkbp:isNonOrientable true
gptkbp:isomorphicTo the sphere with a cross-cap
gptkbp:isQuotientOf the 2-sphere by identifying antipodal points
gptkbp:relatedTo gptkb:Klein_bottle
gptkb:geometry
gptkb:complex_projective_plane
gptkb:Möbius_strip
2-sphere
gptkbp:represents gptkb:RP^2
gptkbp:usedIn gptkb:algebraic_geometry
gptkb:geometry
gptkb:topology
gptkbp:bfsParent gptkb:Donald_Coxeter
gptkbp:bfsLayer 7