Overview

A function represents a mapping from a set of elements, called the domain, to another set of elements, called the range. It is a central notion in mathematics, and has had multiple definitions over time. However, the Set Theory Definition has come to be the standard definition in abstract mathematics.

Classical Analysis

• Function Spaces
  • Banach Spaces - a standard space that can represent function space well. Generally required for doing the basics of analysis.
  • Hilbert Spaces - function spaces with Lebesgue measure also form Hilbert spaces, which are critical spaces in many areas of mathematics and physics.
• Operator Theory

Additional Function Topics

• Arity - classifies a function by the number of arguments
• Category Theory - represents an algebra of functions
• Lambda Calculus - used in computer science to represent function computation.
• Generalized Functions
• Approximation Theory