Glicksberg fixed-point theorem
E23636
The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Glicksberg fixed-point theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T179306 — 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: Glicksberg fixed-point theorem Context triple: [Kakutani fixed-point theorem, relatedTo, Glicksberg fixed-point theorem]
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A.
Kakutani fixed-point theorem
The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
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B.
Brouwer fixed-point theorem
The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
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C.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
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D.
Janet–Cartan theorem
The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
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E.
Kalai–Smorodinsky bargaining solution
The Kalai–Smorodinsky bargaining solution is a cooperative game theory concept that selects a fair agreement between parties by preserving proportional gains relative to their best possible outcomes.
- 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: Glicksberg fixed-point theorem Target entity description: The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
-
A.
Kakutani fixed-point theorem
The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
-
B.
Brouwer fixed-point theorem
The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
-
C.
Nash embedding theorem
The Nash embedding theorem is a fundamental result in differential geometry that shows any Riemannian manifold can be isometrically embedded into some Euclidean space, thereby realizing abstract curved spaces as concrete subsets of standard Euclidean space.
-
D.
Janet–Cartan theorem
The Janet–Cartan theorem is a fundamental result in differential geometry stating that any real-analytic Riemannian manifold can be locally isometrically embedded into a Euclidean space of sufficiently high dimension.
-
E.
Kalai–Smorodinsky bargaining solution
The Kalai–Smorodinsky bargaining solution is a cooperative game theory concept that selects a fair agreement between parties by preserving proportional gains relative to their best possible outcomes.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
fixed-point theorem
ⓘ
theorem in functional analysis ⓘ |
| appliesTo |
compact convex subsets of locally convex topological vector spaces
ⓘ
set-valued maps ⓘ |
| assumptionOnDomain | nonempty compact convex subset ⓘ |
| assumptionOnMap |
nonempty convex compact values
ⓘ
upper semicontinuous set-valued map ⓘ |
| assumptionOnSpace | locally convex topological vector space ⓘ |
| concerns | existence of fixed points ⓘ |
| extends | Kakutani fixed-point theorem ⓘ |
| field |
functional analysis
ⓘ
topological vector spaces ⓘ |
| generalizes |
Kakutani fixed-point theorem to infinite-dimensional settings
ⓘ
linked to:
Kakutani fixed-point theorem
|
| guarantees | existence of a fixed point for the set-valued map ⓘ |
| hasApplication | existence of Nash equilibria in games with infinitely many strategies ⓘ |
| holdsIn | Hausdorff locally convex topological vector spaces ⓘ |
| isPartOf | fixed-point theory in locally convex spaces ⓘ |
| namedAfter | Irving Glicksberg ⓘ |
| relatedTo |
Brouwer fixed-point theorem
ⓘ
Kakutani fixed-point theorem ⓘ Schauder fixed-point theorem ⓘ |
| requires |
closed graph or upper semicontinuity conditions on the correspondence
ⓘ
compactness of the domain set ⓘ convexity of the domain set ⓘ |
| topic |
multifunctions
ⓘ
topological fixed-point theory ⓘ |
| usedIn |
equilibrium existence proofs
ⓘ
game theory ⓘ mathematical economics ⓘ noncooperative game theory ⓘ |
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: Glicksberg fixed-point theorem Description of subject: The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.