n-dimensional real Euclidean space

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Euclidean_space
gptkbp:alsoKnownAs	R^n
gptkbp:application	gptkb:computer_graphics gptkb:geometry gptkb:machine_learning engineering physics statistics
gptkbp:automorphismGroup	gptkb:orthogonal_group
gptkbp:basisFor	standard basis
gptkbp:cardinality	gptkb: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
gptkbp:innerProduct	dot product
gptkbp:isClosedSubsetOf	itself
gptkbp:isContractible	yes
gptkbp:isHausdorff	yes
gptkbp:isHomogeneous	yes
gptkbp:isLocallyCompact	yes
gptkbp:isManifold	yes
gptkbp:isometry	gptkb:translator reflection 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 gptkb:inner_product_space gptkb:normed_space
gptkbp:topology	gptkb:Euclidean_topology
gptkbp:bfsParent	gptkb:SO(n)
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	n-dimensional real Euclidean space