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Cofinal set

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2010 Mathematics Subject Classification: Primary: 06A [MSN][ZBL]

in a partially ordered set $(A,{<})$

A subset $B$ of $(A,{<})$ with the property that for every $a \in A$ there is $b \in B$ such that $a \le b$. Dually, a co-initial set $B$ has the property that for every $a \in A$ there is $b \in B$ such that $b \le a$.

References

  • R. Fraïssé, Theory of Relations, Studies in Logic and the Foundations of Mathematics, Elsevier (2011) p.44. ISBN 0080960413
How to Cite This Entry:
Cofinal set. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cofinal_set&oldid=35006