topologicalStatement
P59517
predicate
Indicates that a statement expresses a relationship or property defined in terms of topological concepts such as continuity, openness, closeness, or convergence.
Observed surface forms (4)
- topologicalProperty ×8
- topologyInduced ×4
- hasTopologicalProperty ×3
- topologyProperty ×2
Sample triples (18)
| Subject | Object |
|---|---|
| Banach limit | element of the dual space (ℓ∞)∗ via predicate surface "topologicalProperty" ⓘ |
| Bernstein set | not Borel measurable via predicate surface "topologicalProperty" ⓘ |
| Bernstein set | not F_sigma via predicate surface "topologicalProperty" ⓘ |
| Bernstein set | not G_delta via predicate surface "topologicalProperty" ⓘ |
| Cantor set | every point is a limit point via predicate surface "topologyProperty" ⓘ |
| Cantor set | no isolated points via predicate surface "topologyProperty" ⓘ |
|
Chebyshev distance (L-infinity metric)
surface form:
Chebyshev distance
|
same as L1 metric on R^n via predicate surface "topologyInduced" ⓘ |
|
Chebyshev distance (L-infinity metric)
surface form:
Chebyshev distance
|
same as L2 metric on R^n via predicate surface "topologyInduced" ⓘ |
| Grassmann manifolds | compact via predicate surface "topologicalProperty" ⓘ |
| Grassmann manifolds | connected via predicate surface "topologicalProperty" ⓘ |
| Grassmann manifolds | simply connected for complex Grassmannians via predicate surface "topologicalProperty" ⓘ |
| Kolmogorov distance | weak convergence of probability measures on the real line via predicate surface "topologyInduced" ⓘ |
|
Liouville numbers
surface form:
Liouville number
|
dense in the real numbers via predicate surface "topologicalProperty" ⓘ |
| Lévy–Prokhorov metric | weak topology on probability measures via predicate surface "topologyInduced" ⓘ |
| Penrose triangle | non-realizable in 3D Euclidean space via predicate surface "hasTopologicalProperty" ⓘ |
| Weierstrass approximation theorem | polynomials are dense in the space of continuous functions on a compact interval ⓘ |
| Whitney umbrella | locally homeomorphic to a plane away from the singular set via predicate surface "hasTopologicalProperty" ⓘ |
| Whitney umbrella | not a 2-manifold at the pinch point via predicate surface "hasTopologicalProperty" ⓘ |