Triple

T16474858
Position Surface form Disambiguated ID Type / Status
Subject Tychonoff theorem for products of compact spaces E400161 entity
Predicate usedIn P98 FINISHED
Object functional analysis
Functional analysis is a branch of mathematics that studies vector spaces with additional structure (such as norms or inner products) and the linear operators acting on them, often using tools from topology and measure theory.
 E1215848 NE FINISHED

Disambiguation candidates (2 decisions)

The exact options the model was shown at each disambiguation step, with the option it chose highlighted — the evidence behind this triple's disambiguated ids.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: functional analysis
Context triple: [Tychonoff theorem for products of compact spaces, usedIn, functional analysis]
  • A. 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.
  • 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. Applied Functional Analysis
    Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
  • D. 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.
  • E. Banach algebra
    A Banach algebra is a complete normed vector space equipped with a compatible associative algebra multiplication, allowing analysis and algebra to be combined in a single structure.
  • 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: functional analysis
Target entity description: Functional analysis is a branch of mathematics that studies vector spaces with additional structure (such as norms or inner products) and the linear operators acting on them, often using tools from topology and measure theory.
  • A. 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.
  • 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. Applied Functional Analysis
    Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
  • D. 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.
  • E. Banach algebra
    A Banach algebra is a complete normed vector space equipped with a compatible associative algebra multiplication, allowing analysis and algebra to be combined in a single structure.
  • F. None of above. chosen

Provenance (5 batches)

Stage Batch ID Job type Status
creating batch_69d883813098819084f5409539723b59 elicitation completed
NER batch_69e32dd32e048190a9eadd32d6b9374c ner completed
NED1 batch_6a004f5f238881909b5f2fb41da3f932 ned_source_triple completed
NED2 batch_6a005447f1948190a939c0051891e444 ned_description completed
NEDg batch_6a00509164cc8190a381ba0a1de95ed1 nedg completed
Created at: April 10, 2026, 5:13 a.m.