Definition:Chain (Set Theory)
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Definition
A totally ordered subset $T$ of a poset $\left({S, \preceq}\right)$ is called a chain in $S$.
A totally ordered set is itself a chain in its own right.
Sources
- Paul R. Halmos: Naive Set Theory (1960)... (previous)... (next): $\S 16$: Zorn's Lemma
- Steven A. Gaal: Point Set Topology (1964)... (previous)... (next): Introduction to Set Theory: $3$. The Axiom of Choice and Its Equivalents
- T.S. Blyth: Set Theory and Abstract Algebra (1975): $\S 7$
