|
gptkbp:instanceOf
|
gptkb:mathematical_concept
gptkb:topology
|
|
gptkbp:borders
|
none
|
|
gptkbp:canBeDefinedByEquation
|
x^2 + y^2 = 1
|
|
gptkbp:canBeEmbeddedIn
|
R^2
|
|
gptkbp:category
|
gptkb:topology
complex analysis
differential geometry
group theory
manifold theory
|
|
gptkbp:compact
|
true
|
|
gptkbp:coveringSpaceOf
|
itself
|
|
gptkbp:dimensions
|
1
|
|
gptkbp:Euler_characteristic
|
0
|
|
gptkbp:fundamentalGroup
|
Z
|
|
gptkbp:hasConnection
|
false
true
|
|
gptkbp:homologyGroupH0
|
Z
|
|
gptkbp:homologyGroupH1
|
Z
|
|
gptkbp:homologyGroupHn
|
0 for n>1
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
circle (S^1)
|
|
gptkbp:isClosed
|
true
|
|
gptkbp:isHausdorff
|
true
|
|
gptkbp:isHomogeneousSpace
|
true
|
|
gptkbp:isLocallyEuclidean
|
true
|
|
gptkbp:isManifold
|
true
|
|
gptkbp:isMatrixGroup
|
true
|
|
gptkbp:isMetricSpace
|
true
|
|
gptkbp:isomorphicTo
|
gptkb:R/Z
unit circle in C
|
|
gptkbp:isOrientable
|
true
|
|
gptkbp:isPathConnected
|
true
|
|
gptkbp:LieGroupType
|
gptkb:U(1)
|
|
gptkbp:parameter
|
(cos θ, sin θ), θ in [0, 2π)
|
|
gptkbp:universalCover
|
real line (R)
|
|
gptkbp:bfsParent
|
gptkb:3-sphere
|
|
gptkbp:bfsLayer
|
6
|