Function Theory

• Functions

  • Overview

  • Definition

• Function

  • x ↦ f (x)

• Examples by domain and codomain

  • X → BB → XBn → B

  • X → ZZ → X

  • X → RR → XRn → X

  • X → CC → XCn → X

• Classes/properties

  • Constant

  • Identity

  • Linear

  • Polynomial

  • Rational

  • Algebraic

  • Analytic

  • Smooth

  • Continuous

  • Measurable

  • Relations (*ectivity)

    • Injective (one-to-one)

    • Surjective (onto)

    • Bijective (one-to-one correspondence, invertible function)

• Constructions   Restriction · Composition · λ · Inverse

• Generalizations   Partial · Multivalued · Implicit