Statements (80)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
gptkb:topology |
| gptkbp:alternativeName |
simplicial_complex
|
| gptkbp:component |
simplex
|
| gptkbp:definedIn |
a set of simplices that satisfies certain intersection properties
|
| gptkbp:dimensions |
maximum dimension of its simplices
|
| gptkbp:example |
gptkb:butter
gptkb:geometry gptkb:Čech_complex gptkb:Vietoris–Rips_complex gptkb:flag_complex gptkb:real_projective_plane gptkb:Eilenberg–MacLane_space Grassmannian clique complex complex projective space triangulation of a surface |
| gptkbp:field |
gptkb:geometry
gptkb:topology combinatorics |
| gptkbp:generalizes |
gptkb:Polygon
graph CW complex |
| gptkbp:hasApplication |
data analysis
robotics image processing sensor networks network science calculation of cohomology calculation of homology calculation of homotopy groups |
| gptkbp:hasConstructionStep |
attaching cells
|
| gptkbp:hasProperty |
gptkb:Hausdorff
finite or infinite Cell abstract or geometric built inductively closed under taking faces finite or countable cells locally contractible |
| gptkbp:hasTopology |
weak topology
|
| gptkbp:hasType |
n-cell
|
| gptkbp:introduced |
gptkb:Henri_Poincaré
gptkb:J._H._C._Whitehead |
| gptkbp:relatedConcept |
gptkb:homotopy_equivalence
gptkb:topology gptkb:cellular_approximation_theorem gptkb:bone gptkb:Whitehead_theorem CW complex homotopy type mapping cone mapping cylinder cellular homology nerve of a cover CW pair CW spectrum attaching map cellular chain complex cellular cohomology cellular decomposition cellular map cellular space finite CW complex finite type CW complex homotopy extension property infinite CW complex regular CW complex simplicial set subcomplex |
| gptkbp:standsFor |
gptkb:Closure-finite_Weak_topology_complex
|
| gptkbp:used_in |
gptkb:geometry
gptkb:cohomology_theory gptkb:persistent_homology topological data analysis mesh generation |
| gptkbp:usedFor |
homotopy theory
|
| gptkbp:usedIn |
gptkb:topology
|
| gptkbp:bfsParent |
gptkb:Topology
|
| gptkbp:bfsLayer |
5
|