Hausdorff metric
E608816
The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Hausdorff metric canonical | 2 |
| Gromov–Hausdorff convergence | 1 |
| Hausdorff distance | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6660374 — 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: Hausdorff metric Context triple: [Felix Hausdorff, knownFor, Hausdorff metric]
-
A.
Banach–Mazur distance
The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
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B.
Carathéodory metric
The Carathéodory metric is an intrinsic distance function in complex analysis that measures how far apart points are in a domain based on holomorphic mappings into the unit disk.
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C.
Kolmogorov distance
Kolmogorov distance is a statistical metric that measures the maximum difference between two cumulative distribution functions, commonly used to quantify convergence in distribution and in goodness-of-fit tests.
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D.
Hausdorff
Hausdorff is a topological separation property requiring that any two distinct points in a space can be enclosed in disjoint open sets.
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E.
Euclidean metric
The Euclidean metric is the standard distance function on Euclidean space, defined by the square root of the sum of squared coordinate differences between two points.
- 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: Hausdorff metric Target entity description: The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
-
A.
Banach–Mazur distance
The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
-
B.
Carathéodory metric
The Carathéodory metric is an intrinsic distance function in complex analysis that measures how far apart points are in a domain based on holomorphic mappings into the unit disk.
-
C.
Kolmogorov distance
Kolmogorov distance is a statistical metric that measures the maximum difference between two cumulative distribution functions, commonly used to quantify convergence in distribution and in goodness-of-fit tests.
-
D.
Hausdorff
Hausdorff is a topological separation property requiring that any two distinct points in a space can be enclosed in disjoint open sets.
-
E.
Euclidean metric
The Euclidean metric is the standard distance function on Euclidean space, defined by the square root of the sum of squared coordinate differences between two points.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
distance function
ⓘ
mathematical concept ⓘ metric ⓘ |
| alternativeName |
Hausdorff distance
NERFINISHED
ⓘ
Pompeiu–Hausdorff metric NERFINISHED ⓘ |
| applicableTo |
closed and bounded subsets of a complete metric space
ⓘ
compact subsets of Euclidean space ⓘ |
| category | metric on sets ⓘ |
| codomain | nonnegative real numbers ⓘ |
| construction | based on supremum of point-to-set distances ⓘ |
| definedOn |
set of compact subsets of a metric space
ⓘ
set of nonempty closed subsets of a metric space ⓘ |
| domain | subsets of a metric space ⓘ |
| enables |
definition of completeness of hyperspaces
ⓘ
study of stability of attractors in dynamical systems ⓘ |
| field |
computer vision
ⓘ
functional analysis ⓘ image processing ⓘ metric geometry ⓘ shape analysis ⓘ topology ⓘ |
| mathematicalArea |
general topology
ⓘ
metric space theory ⓘ |
| measures |
distance between subsets
ⓘ
how far two subsets are from each other ⓘ |
| namedAfter | Felix Hausdorff NERFINISHED ⓘ |
| property |
equals zero if and only if sets are equal (for closed sets)
ⓘ
nonnegative ⓘ satisfies triangle inequality ⓘ symmetric ⓘ |
| relatedConcept |
Gromov–Hausdorff distance
NERFINISHED
ⓘ
Kuratowski convergence of sets NERFINISHED ⓘ Vietoris topology NERFINISHED ⓘ |
| requires | underlying metric space ⓘ |
| symbol | d_H ⓘ |
| topologicalRole |
induces topology on hyperspace of closed subsets
ⓘ
turns space of nonempty compact subsets into a metric space ⓘ |
| usedIn |
approximation of sets by polyhedra
ⓘ
continuity of set-valued maps ⓘ convergence of sets ⓘ fractal geometry ⓘ geometric modeling ⓘ object matching in images ⓘ pattern recognition ⓘ shape comparison ⓘ |
| uses | supremum over one set of infimum distances to the other set ⓘ |
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: Hausdorff metric Description of subject: The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Hausdorff distance
this entity surface form:
Gromov–Hausdorff convergence