TeXipedia

bigsqcup

Represents a large disjoint union operator commonly used in set theory and mathematical notation.

Overview

Serves as an n-ary operator indicating the union of multiple sets where all elements are distinct and no overlapping occurs between sets. Most frequently encountered in:

  • Advanced set theory to denote collection of disjoint sets
  • Abstract algebra for direct sum decompositions
  • Mathematical logic when describing partitions
  • Category theory for coproduct operations

The enlarged size makes it particularly suitable for displaying operations over multiple terms or when emphasizing the disjoint nature of a union in displayed equations.

Examples

Disjoint union of sets over an index

⨆i=1nAi=A1⊔A2⊔⋯⊔An\bigsqcup_{i=1}^n A_i = A_1 \sqcup A_2 \sqcup \cdots \sqcup A_n 
\bigsqcup_{i=1}^n A_i = A_1 \sqcup A_2 \sqcup \cdots \sqcup A_n

Disjoint union of vector spaces

V=⨆λ∈ΛVλV = \bigsqcup_{\lambda \in \Lambda} V_\lambda 
V = \bigsqcup_{\lambda \in \Lambda} V_\lambda

Decomposition of a topological space into connected components

X=⨆α∈IXαX = \bigsqcup_{\alpha \in I} X_\alpha 
X = \bigsqcup_{\alpha \in I} X_\alpha