Functional Analysis

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.

Topics


  • Arity - classifies a function by the number of arguments
  • Category Theory - represents an algebra of functions
  • Banach Spaces - functions with integraion form a Banach space
  • Hibert Spaces - function spaces with Lebesgue measure form Hilbert spaces, which are critical spaces in many areas of mathematics and physics.
  • Lambda Calculus - used in computer science to represent function computation.

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