TeXipedia

doublecup

Represents the binary operation of double union, commonly used in set theory and abstract algebra.

Overview

Serves as a specialized notation in advanced mathematical contexts where standard union operations need to be distinguished or extended. Most frequently encountered in:

  • Abstract algebra for specialized algebraic structures
  • Advanced set theory applications
  • Mathematical logic and formal systems
  • Category theory when dealing with specific types of joins

Typically appears in academic papers and advanced mathematical texts where precise distinction between different types of union operations is essential.

Examples

Expressing the union of three sets using double cup notation.

A⋓B⋓CA \doublecup B \doublecup C 
A \doublecup B \doublecup C

Showing the disjoint union of probability spaces.

(Ω1,F1)⋓(Ω2,F2)(\Omega_1, \mathcal{F}_1) \doublecup (\Omega_2, \mathcal{F}_2) 
(\Omega_1, \mathcal{F}_1) \doublecup (\Omega_2, \mathcal{F}_2)

Representing the disjoint union of topological spaces.

X⋓Y=∐i∈{1,2}XiX \doublecup Y = \coprod_{i \in \{1,2\}} X_i 
X \doublecup Y = \coprod_{i \in \{1,2\}} X_i