restriction
Denotes the restriction of a function to a specific domain or subset, commonly used in mathematical analysis and set theory.
Overview
Essential in advanced mathematics for specifying when a function is being considered only on a particular subset of its domain. Common applications include:
- Defining piecewise functions and their properties
- Analyzing function behavior on specific intervals or subsets
- Proving local properties of functions
- Working with function spaces and topology
Particularly prevalent in real and complex analysis, where examining function behavior on restricted domains is fundamental to understanding continuity, differentiability, and other properties.
Examples
Defining a function restriction to a subset.
f\restriction_A: A \to \mathbb{R}Specifying the restriction of a continuous function to an interval.
g\restriction_{[0,1]}: [0,1] \to \mathbb{R}Showing a map restriction in group theory.
\phi\restriction_H: H \to G