Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

46Gxx Measures and integration in abstract settings

This subtopic studies measures and integration in abstract settings, extending measure theory to functional-analytic and topological contexts.

Specific topics

46G05 Derivatives of functions in infinite-dimensional spaces

Overview

This topic studies derivatives of functions in infinite-dimensional spaces in the setting of measures and integration in abstract settings, with emphasis on foundational results, operator behavior, and analytic applications.

Related Wikipedia Page

Functional analysis (Wikipedia)

Useful Links

Key Ideas

  • Structural properties of the underlying analytic objects
  • Continuity, boundedness, and convergence principles
  • Interaction between abstract theory and computational/application contexts

Typical Uses

Used in research and advanced applications involving measures and integration in abstract settings, including representation, solvability, and stability analysis.

Applications

  • Functional and harmonic analysis
  • Operator and algebraic methods
  • Mathematical physics and PDE models

References

Recommended Textbooks

46G10 Vector-valued measures and integration

Overview

This topic studies vector-valued measures and integration in the setting of measures and integration in abstract settings, with emphasis on foundational results, operator behavior, and analytic applications.

Related Wikipedia Page

Functional analysis (Wikipedia)

Useful Links

Key Ideas

  • Structural properties of the underlying analytic objects
  • Continuity, boundedness, and convergence principles
  • Interaction between abstract theory and computational/application contexts

Typical Uses

Used in research and advanced applications involving measures and integration in abstract settings, including representation, solvability, and stability analysis.

Applications

  • Functional and harmonic analysis
  • Operator and algebraic methods
  • Mathematical physics and PDE models

References

Recommended Textbooks

46G12 Measures and integration on abstract product spaces

Overview

This topic studies measures and integration on abstract product spaces in the setting of measures and integration in abstract settings, with emphasis on foundational results, operator behavior, and analytic applications.

Related Wikipedia Page

Functional analysis (Wikipedia)

Useful Links

Key Ideas

  • Structural properties of the underlying analytic objects
  • Continuity, boundedness, and convergence principles
  • Interaction between abstract theory and computational/application contexts

Typical Uses

Used in research and advanced applications involving measures and integration in abstract settings, including representation, solvability, and stability analysis.

Applications

  • Functional and harmonic analysis
  • Operator and algebraic methods
  • Mathematical physics and PDE models

References

Recommended Textbooks

46G15 Functional analytic lifting theory

Overview

This topic studies functional analytic lifting theory in the setting of measures and integration in abstract settings, with emphasis on foundational results, operator behavior, and analytic applications.

Related Wikipedia Page

Functional analysis (Wikipedia)

Useful Links

Key Ideas

  • Structural properties of the underlying analytic objects
  • Continuity, boundedness, and convergence principles
  • Interaction between abstract theory and computational/application contexts

Typical Uses

Used in research and advanced applications involving measures and integration in abstract settings, including representation, solvability, and stability analysis.

Applications

  • Functional and harmonic analysis
  • Operator and algebraic methods
  • Mathematical physics and PDE models

References

Recommended Textbooks

46G20 Infinite-dimensional holomorphy

Overview

This topic studies infinite-dimensional holomorphy in the setting of measures and integration in abstract settings, with emphasis on foundational results, operator behavior, and analytic applications.

Related Wikipedia Page

Functional analysis (Wikipedia)

Useful Links

Key Ideas

  • Structural properties of the underlying analytic objects
  • Continuity, boundedness, and convergence principles
  • Interaction between abstract theory and computational/application contexts

Typical Uses

Used in research and advanced applications involving measures and integration in abstract settings, including representation, solvability, and stability analysis.

Applications

  • Functional and harmonic analysis
  • Operator and algebraic methods
  • Mathematical physics and PDE models

References

Recommended Textbooks

46G25 (Spaces of) multilinear mappings and polynomials

Overview

This topic studies (spaces of) multilinear mappings and polynomials in the setting of measures and integration in abstract settings, with emphasis on foundational results, operator behavior, and analytic applications.

Related Wikipedia Page

Functional analysis (Wikipedia)

Useful Links

Key Ideas

  • Structural properties of the underlying analytic objects
  • Continuity, boundedness, and convergence principles
  • Interaction between abstract theory and computational/application contexts

Typical Uses

Used in research and advanced applications involving measures and integration in abstract settings, including representation, solvability, and stability analysis.

Applications

  • Functional and harmonic analysis
  • Operator and algebraic methods
  • Mathematical physics and PDE models

References

Recommended Textbooks