Foundations of Modern Analysis
E889766
Foundations of Modern Analysis is a classic graduate-level textbook that systematically develops modern mathematical analysis using rigorous, abstract methods and functional analysis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Foundations of Modern Analysis canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10848540 — 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: Foundations of Modern Analysis Context triple: [Jean Dieudonné, notableWork, Foundations of Modern Analysis]
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A.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
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B.
Foundations of Functional Analysis
Foundations of Functional Analysis is a seminal mathematical text that systematically develops the core concepts and theorems of functional analysis, particularly in the tradition of the Riesz school.
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C.
Leçons d’analyse fonctionnelle
Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
-
D.
Problems and Theorems in Analysis (with George Pólya)
"Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
-
E.
Fondamenti per la teorica delle funzioni di variabili reali
Fondamenti per la teorica delle funzioni di variabili reali is a foundational mathematical treatise by Ulisse Dini that helped formalize real analysis and the theory of real-valued functions.
- 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: Foundations of Modern Analysis Target entity description: Foundations of Modern Analysis is a classic graduate-level textbook that systematically develops modern mathematical analysis using rigorous, abstract methods and functional analysis.
-
A.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
-
B.
Foundations of Functional Analysis
Foundations of Functional Analysis is a seminal mathematical text that systematically develops the core concepts and theorems of functional analysis, particularly in the tradition of the Riesz school.
-
C.
Leçons d’analyse fonctionnelle
Leçons d’analyse fonctionnelle is a foundational textbook in functional analysis that helped shape the modern theory of linear operators and Banach and Hilbert spaces.
-
D.
Problems and Theorems in Analysis (with George Pólya)
"Problems and Theorems in Analysis (with George Pólya)" is a classic two-volume collection of challenging problems and results in mathematical analysis that has become a standard reference and training resource for advanced students and researchers.
-
E.
Fondamenti per la teorica delle funzioni di variabili reali
Fondamenti per la teorica delle funzioni di variabili reali is a foundational mathematical treatise by Ulisse Dini that helped formalize real analysis and the theory of real-valued functions.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
graduate-level textbook
ⓘ
mathematics textbook ⓘ |
| approach |
abstract
ⓘ
axiomatic ⓘ |
| author | Jean Dieudonné NERFINISHED ⓘ |
| basedOn | Éléments d’analyse NERFINISHED ⓘ |
| classification | nonfiction book ⓘ |
| contains | numerous exercises ⓘ |
| countryOfOrigin | France ⓘ |
| coversTopic |
Banach spaces
NERFINISHED
ⓘ
Hilbert spaces NERFINISHED ⓘ abstract integration ⓘ differentiation in Banach spaces ⓘ functional analysis ⓘ integration theory ⓘ linear operators ⓘ measure theory ⓘ metric spaces ⓘ normed spaces ⓘ spectral theory basics ⓘ topological vector spaces ⓘ topology ⓘ |
| emphasizes |
general theorems over special cases
ⓘ
structure of topological and normed spaces ⓘ |
| field |
functional analysis
ⓘ
mathematical analysis ⓘ |
| hasAuthorAffiliation | Bourbaki school of mathematics NERFINISHED ⓘ |
| influenced | modern curricula in analysis ⓘ |
| language | English ⓘ |
| level | graduate ⓘ |
| originalLanguage | French ⓘ |
| partOfSeries | Elements of Mathematics NERFINISHED ⓘ |
| publicationYear | 1960s ⓘ |
| publisher | Academic Press NERFINISHED ⓘ |
| style | rigorous ⓘ |
| targetAudience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ |
| usedAs | reference for functional analysis ⓘ |
| volumeInSeries | 1 ⓘ |
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: Foundations of Modern Analysis Description of subject: Foundations of Modern Analysis is a classic graduate-level textbook that systematically develops modern mathematical analysis using rigorous, abstract methods and functional analysis.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.