Whitney umbrella
E285918
example in differential topology
mathematical surface
real algebraic variety
singular algebraic surface
singularity model
The Whitney umbrella is a classic example of a singular algebraic surface in three-dimensional space, notable in differential topology for its pinch point singularity.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Whitney umbrella canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2652910 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Whitney umbrella Context triple: [Hassler Whitney, hasConceptNamedAfter, Whitney umbrella]
-
A.
Whitney
Whitney is a common English surname most famously associated with Eli Whitney, the American inventor of the cotton gin.
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B.
Whitney
Whitney is an unincorporated community and census-designated place in the Las Vegas Valley of Clark County, Nevada.
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C.
Whitney
Whitney is the multi-platinum 1987 studio album by Whitney Houston that solidified her status as a global pop and R&B superstar.
-
D.
Hyacinth
Hyacinth is a given name of Greek origin, historically associated with mythological and floral imagery and used for people of any gender.
-
E.
Rosa
Rosa is a genus of flowering plants known for its ornamental roses, prized worldwide for their beauty, fragrance, and cultural symbolism.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Whitney umbrella Target entity description: The Whitney umbrella is a classic example of a singular algebraic surface in three-dimensional space, notable in differential topology for its pinch point singularity.
-
A.
Whitney
Whitney is an unincorporated community and census-designated place in the Las Vegas Valley of Clark County, Nevada.
-
B.
Whitney
Whitney is the multi-platinum 1987 studio album by Whitney Houston that solidified her status as a global pop and R&B superstar.
-
C.
Whitney
Whitney is a common English surname most famously associated with Eli Whitney, the American inventor of the cotton gin.
-
D.
Hyacinth
Hyacinth is a given name of Greek origin, historically associated with mythological and floral imagery and used for people of any gender.
-
E.
Rosa
Rosa is a genus of flowering plants known for its ornamental roses, prized worldwide for their beauty, fragrance, and cultural symbolism.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
example in differential topology
ⓘ
mathematical surface ⓘ real algebraic variety ⓘ singular algebraic surface ⓘ singularity model ⓘ |
| appearsInField |
differential topology
ⓘ
real algebraic geometry ⓘ singularity theory ⓘ |
| hasComplexification | complex surface defined by x^2 = y^2 z in C^3 ⓘ |
| hasCoordinateDescription | {(x,y,z) in R^3 : x^2 = y^2 z} ⓘ |
| hasCriticalPoint | at the origin for the projection to the base plane ⓘ |
| hasDefiningEquation | x^2 = y^2 z ⓘ |
| hasDimension | 2 ⓘ |
| hasGeometricFeature |
a line of self-intersection ending at a pinch point
ⓘ
a sheet that folds and intersects itself ⓘ |
| hasIsolatedSingularity | at the origin ⓘ |
| hasLocalModelNearSingularity | cross-cap ⓘ |
| hasNameOrigin | shape reminiscent of an umbrella with a pinched handle ⓘ |
| hasParameterDomain | R^2 in the parametrization (u,v) ↦ (uv, u, v^2) ⓘ |
| hasParametrization | (u,v) ↦ (uv, u, v^2) ⓘ |
| hasRealForm | defined over the real numbers ⓘ |
| hasSelfIntersectionAlong | the positive z-axis ⓘ |
| hasSingularityType |
cross-cap singularity
ⓘ
pinch point singularity ⓘ |
| hasSingularSet | the z-axis for z ≥ 0 ⓘ |
| hasTopologicalProperty |
locally homeomorphic to a plane away from the singular set
ⓘ
not a 2-manifold at the pinch point ⓘ |
| isClassicExampleOf |
non-immersed surface in R^3
ⓘ
singular surface in R^3 ⓘ surface with pinch point ⓘ |
| isDiscussedIn |
textbooks on differential topology
ⓘ
textbooks on singularity theory ⓘ |
| isEmbeddedIn |
R^3
ⓘ
three-dimensional Euclidean space ⓘ |
| isNamedAfter | Hassler Whitney ⓘ |
| isUsedAsCounterexampleTo | naive generalizations of manifold properties to singular varieties ⓘ |
| isUsedToIllustrate |
behavior of pinch point singularities
ⓘ
failure of local Euclidean structure at singularities ⓘ non-manifold points on algebraic surfaces ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Whitney umbrella Description of subject: The Whitney umbrella is a classic example of a singular algebraic surface in three-dimensional space, notable in differential topology for its pinch point singularity.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.