# Linked set

In mathematics, an **upwards linked set** *A* is a subset of a partially ordered set, *P*, in which any two of elements *A* have a common upper bound in *P*. Similarly, every pair of elements of a **downwards linked set** has a lower bound. Every centered set is linked, which includes, in particular, every directed set.

## References

- Fremlin, David H. (1984).
*Consequences of Martin's axiom*. Cambridge tracts in mathematics, no. 84. Cambridge: Cambridge University Press. ISBN 0-521-25091-9.

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