Centered set
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In mathematics, an upwards centered set A is a subset of a partially ordered set P, such that any finite subset of A has an upper bound in P. Similarly, any finite subset of a downwards centered set has a lower bound. Note that any directed set is necessarily centered, and any centered set is linked.
A subset B of a partial order is said to be σ-centered if it is a countable union of centered sets.
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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