TeXipedia

imageof

Denotes the image of a function or mapping in mathematical contexts, particularly in set theory and abstract algebra.

Overview

Essential in advanced mathematics for describing the output range or codomain values that result from applying a function to its domain.

  • Commonly used in set theory to specify the set of all output values
  • Appears frequently in linear algebra when discussing transformations
  • Important in category theory and abstract algebra for describing morphisms
  • Helps visualize and formalize function behavior in mathematical proofs

Examples

Showing the image of a function f mapping X to Y in set theory.

f:X⊷Yf: X \imageof Y 
f: X \imageof Y

Indicating the image of a linear transformation T between vector spaces.

T:V⊷WT: V \imageof W 
T: V \imageof W

Representing a homomorphism between algebraic structures.

ϕ:G⊷H\phi: G \imageof H 
\phi: G \imageof H