Borel–Lebesgue theorem
E1116059
UNEXPLORED
The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Heine–Borel theorem | 2 |
| Borel–Lebesgue theorem canonical | 1 |
| Heine–Borel theorem for products of closed bounded intervals in R | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T14704225 — 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: Borel–Lebesgue theorem Context triple: [Émile Borel, notableWork, Borel–Lebesgue theorem]
-
A.
Arzelà–Ascoli theorem
The Arzelà–Ascoli theorem is a fundamental result in analysis that characterizes the relative compactness of families of functions via uniform boundedness and equicontinuity.
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B.
Bolzano–Weierstrass theorem
The Bolzano–Weierstrass theorem is a fundamental result in real analysis stating that every bounded infinite sequence in ℝⁿ has a convergent subsequence.
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C.
Banach–Alaoglu theorem
The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
-
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.
Krein–Milman theorem
The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme 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: Borel–Lebesgue theorem Target entity description: The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
-
A.
Arzelà–Ascoli theorem
The Arzelà–Ascoli theorem is a fundamental result in analysis that characterizes the relative compactness of families of functions via uniform boundedness and equicontinuity.
-
B.
Bolzano–Weierstrass theorem
The Bolzano–Weierstrass theorem is a fundamental result in real analysis stating that every bounded infinite sequence in ℝⁿ has a convergent subsequence.
-
C.
Banach–Alaoglu theorem
The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
-
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.
Krein–Milman theorem
The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
- F. None of above. chosen
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
Tychonoff theorem for products of compact spaces
→
generalizes
→
Heine–Borel theorem for products of closed bounded intervals in R
ⓘ
linked to: Borel–Lebesgue theorem
linked to: Borel–Lebesgue theorem
linked to: Borel–Lebesgue theorem