n-dimensional real Euclidean space

URI: https://gptkb.org/entity/n-dimensional_real_Euclidean_space
GPTKB entity
Statements (51)
Predicate Object
gptkbp:instanceOf gptkb:Euclidean_space
gptkbp:alsoKnownAs R^n
gptkbp:application gptkb:geometry
gptkb:machine_learning
computer graphics
engineering
physics
statistics
gptkbp:automorphismGroup orthogonal group
gptkbp:basisFor standard basis
gptkbp:cardinality continuum
gptkbp:containsElement n-tuple of real numbers
gptkbp:dimensions n
gptkbp:distanceFunction Euclidean distance
gptkbp:field real numbers
gptkbp:firstDescribed gptkb:Euclid
gptkbp:generalizes gptkb:3-dimensional_Euclidean_space
Euclidean line
Euclidean plane
gptkbp:groupOfIsometries gptkb:Euclidean_group
gptkbp:hasConnection yes
gptkbp:hasSpecialCase finite-dimensional real Hilbert space
gptkbp:hasSubgroup n-dimensional real affine space
https://www.w3.org/2000/01/rdf-schema#label n-dimensional real Euclidean space
gptkbp:innerProduct dot product
gptkbp:isClosedSubsetOf itself
gptkbp:isContractible yes
gptkbp:isHausdorff yes
gptkbp:isHomogeneous yes
gptkbp:isLocallyCompact yes
gptkbp:isManifold yes
gptkbp:isometry reflection
translator
rotation
glide reflection
gptkbp:isOpenSubsetOf itself
gptkbp:isOrientable yes
gptkbp:isParacompact yes
gptkbp:isPathConnected yes
gptkbp:isSecondCountable yes
gptkbp:isSeparable yes
gptkbp:notation R^n
gptkbp:numberOfIssues yes
gptkbp:originatedIn yes
gptkbp:structure gptkb:Vector
gptkb:topology
inner product space
normed space
gptkbp:topology gptkb:Euclidean_topology
gptkbp:bfsParent gptkb:SO(n)
gptkbp:bfsLayer 6