Euclidean space (where the metric is positive-definite)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Euclidean_space gptkb:normed_vector_space gptkb:topology inner product space
gptkbp:basisFor	orthonormal basis
gptkbp:contrastsWith	gptkb:Euclidean_space gptkb:Minkowski_space noncommutative geometry
gptkbp:dimensions	n (arbitrary non-negative integer)
gptkbp:generalizes	Euclidean line Euclidean plane
gptkbp:hasConnection	true
gptkbp:hasDistanceFormula	square root of sum of squares of differences
gptkbp:hasGroupOfIsometries	gptkb:Euclidean_group
gptkbp:hasInnerProduct	dot product
gptkbp:hasMeasure	Lebesgue measure
gptkbp:hasProperty	homogeneous flat geometry isotropic positive-definite metric
gptkbp:hasSpecialCase	gptkb:Hilbert_space real coordinate space
gptkbp:hasStandardNotation	R^n
gptkbp:hasSubspaces	lines planes hyperplanes affine subspaces linear subspaces
gptkbp:hasTopology	standard topology
gptkbp:hasVolumeElement	dx1 dx2 ... dxn
https://www.w3.org/2000/01/rdf-schema#label	Euclidean space (where the metric is positive-definite)
gptkbp:includesMetric	Euclidean metric
gptkbp:isHausdorff	true
gptkbp:isHomogeneousSpaceOf	gptkb:Euclidean_group
gptkbp:isLocallyCompact	true
gptkbp:isManifold	true
gptkbp:isParacompact	true
gptkbp:isSecondCountable	true
gptkbp:isSeparable	true
gptkbp:isVectorSpaceOver	real numbers
gptkbp:namedAfter	gptkb:Euclid
gptkbp:numberOfIssues	true
gptkbp:usedIn	gptkb:geometry computer graphics engineering physics linear algebra
gptkbp:bfsParent	gptkb:Euclidean_space
gptkbp:bfsLayer	5