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Article | REF: AF94 V1

Ordered Set Theory

Author: Jean-Charles PINOLI

Publication date: August 10, 2019, Review date: May 7, 2021

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4. Special subsets

4.1 Increased and decreased subsets

Definition (bounded above and bounded below). In a partially ordered space (E, ≼) a non-empty subset X is bounded above if it has a majorant, a non-empty subset X is bounded below if it has a minorant, and a non-empty subset X is bounded if it has both a minorant and a majorant (or equivalently, if it is contained in an interval).

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