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.
All labels observed (5)
| Label | Occurrences |
|---|---|
| topologicalProperty | 8 |
| topologyInduced | 4 |
| hasTopologicalProperty | 3 |
| topologyProperty | 2 |
| topologicalStatement canonical | 1 |
Description generation (PDg)
The one-sentence description above was generated by prompting gpt-5.1 with the predicate name and this instruction.
Instruction
Given a predicate that represents a relationship or action between entities, generate a one-sentence description explaining its meaning. # Instructions Focus on describing the relationship, not the entities themselves. # Response Format Begin the description with \' Indicates...\'
Input
Predicate: topologicalStatement
Generated description
Indicates that a statement expresses a relationship or property defined in terms of topological concepts such as continuity, openness, closeness, or convergence.
Sample triples (18)
| Subject | Object |
|---|---|
| Weierstrass approximation theorem | polynomials are dense in the space of continuous functions on a compact interval ⓘ |
| Cantor set | every point is a limit point via predicate surface "topologyProperty" ⓘ |
| Cantor set | no isolated points via predicate surface "topologyProperty" ⓘ |
| Kolmogorov distance | weak convergence of probability measures on the real line via predicate surface "topologyInduced" ⓘ |
| Whitney umbrella | not a 2-manifold at the pinch point via predicate surface "hasTopologicalProperty" ⓘ |
| Whitney umbrella | locally homeomorphic to a plane away from the singular set via predicate surface "hasTopologicalProperty" ⓘ |
| Bernstein set | not F_sigma via predicate surface "topologicalProperty" ⓘ |
| Bernstein set | not G_delta via predicate surface "topologicalProperty" ⓘ |
| Bernstein set | not Borel measurable via predicate surface "topologicalProperty" ⓘ |
| Penrose triangle | non-realizable in 3D Euclidean space via predicate surface "hasTopologicalProperty" ⓘ |
| Banach limit | element of the dual space (ℓ∞)∗ via predicate surface "topologicalProperty" ⓘ |
|
Liouville numbers
surface form:
Liouville number
|
dense in the real numbers via predicate surface "topologicalProperty" ⓘ |
|
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" ⓘ |
| Lévy–Prokhorov metric | weak topology on probability measures via predicate surface "topologyInduced" ⓘ |
| Grassmann manifolds | connected via predicate surface "topologicalProperty" ⓘ |
| Grassmann manifolds | compact via predicate surface "topologicalProperty" ⓘ |
| Grassmann manifolds | simply connected for complex Grassmannians via predicate surface "topologicalProperty" ⓘ |