Statements (43)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
algebraic varieties
vector spaces topological spaces manifolds physical space |
| gptkbp:defines |
the minimum number of coordinates needed to specify a point
the smallest n such that every open cover has a refinement where no point is included in more than n+1 sets (Lebesgue covering dimension) the number of parameters needed to describe a system the cardinality of a basis of a vector space the number of independent directions at a point the exponent in the scaling law for measure (Hausdorff dimension) the maximum length of a chain of prime ideals (Krull dimension) |
| gptkbp:describes |
number of independent parameters or coordinates needed to specify a point
|
| gptkbp:example |
3-dimensional space
n-dimensional space 1-dimensional line 2-dimensional plane |
| gptkbp:hasProperty |
can be finite or infinite
can be fractional (fractal dimension) can be negative (in some contexts) can be zero |
| gptkbp:hasUnit |
none (dimension is a pure number)
|
| gptkbp:hasWikidataID |
Q11423
|
| gptkbp:hasWikipediaPage |
https://en.wikipedia.org/wiki/Dimension
|
| https://www.w3.org/2000/01/rdf-schema#label |
dimension (mathematics)
|
| gptkbp:relatedTo |
gptkb:Euclidean_space
gptkb:Hilbert_space gptkb:Hausdorff_dimension gptkb:Krull_dimension fractal dimension vector space dimension Lebesgue covering dimension |
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:geometry gptkb:machine_learning gptkb:topology computer science data analysis physics linear algebra |
| gptkbp:bfsParent |
gptkb:basis_(mathematics)
|
| gptkbp:bfsLayer |
8
|