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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Bibliography

(1) - ALLAM (A.A), BAKEIR (M.Y.), ABO-TABL (E.A.) - Some methods for generating topologies by relations, - Bulletin of the Malaysian Mathematical Sciences Society, (2), Vol. 31, No.1, pp. 35-45 (2008).
(2) - BALBES (R.), DWINGER (P.) - Distributive Lattices,...

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