The Eigenspace

Part 1: Introduction
- Chapter 1: Definitions
  - circle1.1: Grothendieck Universe
  - circle1.2: Categories
- Chapter 2: Integrals
  - circle2.1: Bochner Integral
Part 2: General Topology
- Chapter 3: Topological Structure
  - circle3.1: Generating Topologies
  - circle3.2: Connectedness
  - circle3.3: Neighbourhoods
  - circle3.4: Filters
  - circle3.5: Continuity
  - circle3.6: Hausdorff
  - circle3.7: Locally Compact Groups
  - circle3.8: Normal Spaces
  - circle3.9: Quotient Topologies
  - circle3.10: Compactness
  - circle3.11: $\s$-Compact Spaces
  - circle3.12: Paracompact Spaces
  - 3.13: Locally Compact Hausdorff Spaces
    circle3.13.6: Paracompactness and LCH Spaces
Part 3: Measure Theory
- Chapter 4: Set Systems
  - circle4.1: Algebras
  - circle4.2: Product $\s$-Algebra
  - circle4.3: Borel $\s$-Algebra
  - circle4.4: Elementary Families
- Chapter 5: Positive Measures
  - circle5.1: Measure Space
  - circle5.2: Complete Measures
  - circle5.3: $\s$-Finite Measures
  - circle5.4: Regular Measures
  - circle5.5: Carathéodory’s Construction
  - circle5.6: Lebesgue-Stieltjes Measure
- Chapter 6: Radon Measures
  - circle6.1: Haar Measure
Part 4: Functional Analysis
- Chapter 7: Locally Convex Space
  - circle7.1: Seminorm
  - circle7.2: Continuous Linear Maps
  - circle7.3: Compact Convex Sets
  - circle7.4: Hahn-Banach Theorem
- Chapter 8: Riemann-Stieltjes Integral
  - circle8.1: Partition
  - circle8.2: Functions of Bounded Variation
  - circle8.3: Riemann-Stieltjes Sums and Integrals
  - circle8.4: Integrators of Bounded Variation
Part 5: Operator Algebra
- Chapter 9: Fundamentals of Banach Algebras and C*-Algebras
  - circle9.1: Banach Algebras
  - circle9.2: Abstract Index
  - circle9.3: Spectrum and Functional Calculus
  - circle9.4: Gelfand Representation of Abelian Banach Algebras
  - circle9.5: Spectrum and Functional Calculus in C*-Algebras
  - circle9.6: Continuity of Homomorphisms
  - circle9.7: Order Structures of $C^{*}$-Algebras
  - circle9.8: Positive Linear Functionals and States
Part 6: Miscellaneous
- circleChapter 10: Combinatorics
Part 7: Notes
- Chapter 11: Measure Theory
  - circle11.1: Introduction
- Chapter 12: Advanced PDE
  - circle12.1: Notations
  - circle12.2: Real (scalar) $1^{st}$ order PDEs
  - circle12.3: Cauchy-Kovalevskaya Theorem
  - circle12.4: Fourier Transforms and Distribution
- Chapter 13: Convex and Nonlinear Analysis
  - circle13.1: Notations
  - circle13.2: Supporting Hyperplanes
  - circle13.3: Hausdorff Distance
  - circle13.4: Polar Bodies
  - circle13.5: Norms and Symmetric Convex Bodies in $\R^{n}$
  - circle13.6: Convex Book

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Recent Changes

circleTheorem 13.5.5: John’s Proposition
circleTheorem 13.1.26: Separating Hyperplane
circleExample 13.1.20: Infinite Dimensional Vector Space
circleTheorem 12.4.19
circleProposition 12.4.18: Volume of Sphere
circleProposition 12.4.17
circleDefinition 12.4.16: Radial Laplacian
circleCorollary 12.4.15
circleProposition 12.4.14: Green’s Identities
circleTheorem 12.4.13

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