Busemann–Feller theorem
E855798
The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Busemann–Feller theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10313547 — 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: Busemann–Feller theorem Context triple: [Herbert Busemann, hasConceptNamedAfter, Busemann–Feller theorem]
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A.
Hopf–Rinow theorem
The Hopf–Rinow theorem is a fundamental result in Riemannian geometry that characterizes when a Riemannian manifold is geodesically complete, relating metric completeness, compactness of closed and bounded sets, and the existence of minimizing geodesics between points.
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B.
Bernstein theorem
Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
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C.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
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D.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
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E.
Carathéodory existence theorem
The Carathéodory existence theorem is a result in the theory of ordinary differential equations that guarantees the existence (and sometimes uniqueness) of solutions under weaker regularity conditions on the right-hand side than those required by classical theorems like Picard–Lindelöf.
- 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: Busemann–Feller theorem Target entity description: The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
-
A.
Hopf–Rinow theorem
The Hopf–Rinow theorem is a fundamental result in Riemannian geometry that characterizes when a Riemannian manifold is geodesically complete, relating metric completeness, compactness of closed and bounded sets, and the existence of minimizing geodesics between points.
-
B.
Bernstein theorem
Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
-
C.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
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D.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
E.
Carathéodory existence theorem
The Carathéodory existence theorem is a result in the theory of ordinary differential equations that guarantees the existence (and sometimes uniqueness) of solutions under weaker regularity conditions on the right-hand side than those required by classical theorems like Picard–Lindelöf.
- F. None of above. chosen
Statements (25)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in geometric measure theory ⓘ |
| appliesTo | metric spaces ⓘ |
| characterizes | geodesic metric spaces ⓘ |
| concerns | existence of shortest paths between points in a metric space ⓘ |
| describes | conditions under which a metric space is geodesic ⓘ |
| field |
geometric measure theory
ⓘ
geometry ⓘ metric geometry ⓘ |
| historicalPeriod | 20th-century mathematics ⓘ |
| implies | existence of geodesics under certain distance conditions ⓘ |
| isPartOf | theory of geodesic metric spaces ⓘ |
| namedAfter |
Herbert Busemann
NERFINISHED
ⓘ
William Feller NERFINISHED ⓘ |
| relatedTo |
Busemann space
NERFINISHED
ⓘ
Hopf–Rinow theorem NERFINISHED ⓘ geodesic space ⓘ length spaces ⓘ |
| relates | distance properties of a metric space to existence of shortest paths ⓘ |
| topic |
geodesics in metric spaces
ⓘ
metric characterization of geodesic spaces ⓘ shortest paths in metric spaces ⓘ |
| usesConcept |
distance function
ⓘ
geodesic ⓘ metric space ⓘ |
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: Busemann–Feller theorem Description of subject: The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.