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Definition: Index Set and Set Family
Let X be an arbitrary set, and let I be a non-empty set, called the index set. A sets family X_{i}{\text{ , }}i\in I is a map I\to \mathcal P(X), where \mathcal P(X) is the power set of X.
Notes
- In other words, each X_i is a subset of X.
- The elements i\in I are called indices of the family of sets X_{i}{\text{ , }}i\in I.
Mentioned in:
Corollaries: 1
Definitions: 2 3 4 5 6 7 8 9 10 11 12 13 14
Proofs: 15 16 17 18
Propositions: 19
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References
Adapted from CC BY-SA 3.0 Sources:
- Brenner, Prof. Dr. rer. nat., Holger: Various courses at the University of Osnabrück