Produits tensoriels topologiques et espaces nucléaires
E254122
"Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Produits tensoriels topologiques et espaces nucléaires canonical | 1 |
| Topological Tensor Products and Nuclear Spaces | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2290632 — 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: Produits tensoriels topologiques et espaces nucléaires Context triple: [Alexander Grothendieck, doctoralThesisTitle, Produits tensoriels topologiques et espaces nucléaires]
-
A.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
-
B.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
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C.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
D.
Topologie (with Heinz Hopf)
"Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
-
E.
Hilbert spaces
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
- 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: Produits tensoriels topologiques et espaces nucléaires Target entity description: "Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
-
A.
L’intégration dans les groupes topologiques et ses applications
L’intégration dans les groupes topologiques et ses applications is a foundational mathematical monograph by André Weil that develops the theory of integration on topological groups and explores its far-reaching applications in analysis and number theory.
-
B.
Méthodes de calcul différentiel absolu et leurs applications
Méthodes de calcul différentiel absolu et leurs applications is a foundational mathematical work that systematically develops the theory of tensor calculus and its applications, laying groundwork later used in general relativity.
-
C.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
D.
Topologie (with Heinz Hopf)
"Topologie" is a foundational 1935 textbook on general topology co-authored by Pavel Alexandrov and Heinz Hopf that helped shape the modern development of the field.
-
E.
Hilbert spaces
Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
doctoral thesis
ⓘ
foundational work in functional analysis ⓘ mathematical work ⓘ |
| academicAdvisor | Laurent Schwartz ⓘ |
| academicDegreeConferred | Doctorat d'État en mathématiques ⓘ |
| academicInstitution |
University of Nancy
ⓘ
surface form:
Université de Nancy
|
| author | Alexander Grothendieck ⓘ |
| authorBirthYear | 1928 ⓘ |
| authorDeathYear | 2014 ⓘ |
| completionYear | 1953 ⓘ |
| countryOfOrigin | France ⓘ |
| field |
functional analysis
ⓘ
nuclear spaces ⓘ topological tensor products ⓘ topological vector spaces ⓘ |
| hasAuthorAtTimeOfWriting | Alexander Grothendieck ⓘ |
| impact |
provided tools for the study of spaces of distributions and test functions
ⓘ
shaped the modern theory of topological tensor products ⓘ |
| influencedField |
distribution theory
ⓘ
modern functional analysis ⓘ operator theory ⓘ theory of Schwartz distributions ⓘ topological vector space theory ⓘ |
| introducedConcept |
injective tensor product of locally convex spaces
ⓘ
nuclear space ⓘ projective tensor product of locally convex spaces ⓘ topological tensor product of locally convex spaces ⓘ |
| isConsidered |
classical reference on nuclear spaces
ⓘ
cornerstone of Grothendieck's early work in analysis ⓘ |
| language | French ⓘ |
| mainResult |
applications of nuclear spaces to distribution theory
ⓘ
construction of topological tensor products with universal properties ⓘ criteria for nuclearity of locally convex spaces ⓘ systematic development of nuclear locally convex spaces ⓘ |
| mainTopic |
characterization of nuclear spaces
ⓘ
structure of locally convex spaces ⓘ tensor products of topological vector spaces ⓘ |
| publicationYear | 1953 ⓘ |
| relatedConcept |
Fréchet space
ⓘ
Montel space ⓘ Schwartz space ⓘ locally convex topological vector space ⓘ |
| relatedMathematician |
Jean Dieudonné
ⓘ
Laurent Schwartz ⓘ Nicolas Bourbaki ⓘ |
| relatedWork |
Generalized Functions (multi-volume series)
ⓘ
surface form:
Théorie des distributions
|
| titleTranslation |
Produits tensoriels topologiques et espaces nucléaires
self-linksurface differs
ⓘ
surface form:
Topological Tensor Products and Nuclear Spaces
|
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: Produits tensoriels topologiques et espaces nucléaires Description of subject: "Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Alexander Grothendieck
→
doctoralThesisTitle
→
Produits tensoriels topologiques et espaces nucléaires
ⓘ
Produits tensoriels topologiques et espaces nucléaires
→
titleTranslation
→
Produits tensoriels topologiques et espaces nucléaires
self-linksurface differs
ⓘ
this entity surface form:
Topological Tensor Products and Nuclear Spaces