Definition:Pairwise Disjoint

Definition

Let $\mathbb S$ be a set of sets such that:

$\forall T_1, T_2 \in \mathbb S: T_1 \cap T_2 = \varnothing$

That is, if the intersection of each pair of sets is empty.

Then the sets in $\mathbb S$ are said to be pairwise disjoint or mutually disjoint.

Sources

• Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 4$: Unions and Intersections
• Richard A. Dean: Elements of Abstract Algebra (1966): $\S 0.2$
• George McCarty: Topology: An Introduction with Application to Topological Groups (1967): $\text{I}$
• A.N. Kolmogorov and S.V. Fomin‎: Introductory Real Analysis (1968): $\S 1.2$
• T.S. Blyth: Set Theory and Abstract Algebra (1975): $\S 6$