# 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
