Definition:Pairwise Disjoint/Family
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Definition
An indexed family of sets $\family {S_i}_{i \mathop \in I}$ is said to be pairwise disjoint if and only if:
- $\forall i, j \in I: i \ne j \implies S_i \cap S_j = \O$
Hence the indexed sets $S_i$ themselves, where $i \in I$, are referred to as being pairwise disjoint.
Also known as
Other names for pairwise disjoint include mutually disjoint and non-intersecting.
Some sources use the compact term disjoint family.
Sources
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Subsets and Complements; Union and Intersection
- 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $1$ Set Theory: $1$. Sets and Functions: $1.2$: Operations on sets
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 6$. Indexed families; partitions; equivalence relations