Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
compact subspaces of spheres
|
| gptkbp:describes |
relationship between homology of a subspace and cohomology of its complement in a sphere
|
| gptkbp:field |
gptkb:topology
|
| gptkbp:firstPublished |
1922
|
| https://www.w3.org/2000/01/rdf-schema#label |
Alexander duality
|
| gptkbp:namedAfter |
gptkb:James_Waddell_Alexander_II
|
| gptkbp:relatedTo |
gptkb:Poincaré_duality
gptkb:Lefschetz_duality |
| gptkbp:sentence |
For a compact subset K of the n-sphere, the reduced homology of the complement is isomorphic to the reduced cohomology of K, up to a degree shift.
|
| gptkbp:usedIn |
gptkb:topology
knot theory manifold theory |
| gptkbp:bfsParent |
gptkb:Poincaré_duality
gptkb:James_Waddell_Alexander_II |
| gptkbp:bfsLayer |
6
|