nLab
upper bound

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Definitions

Definition

For (S,)(S, \leq) a preorder and ASA \hookrightarrow S a subset, an upper bound of AA in SS is an element xx of SS such that yxy \leq x whenever yAy \in A.

Dually (in the opposite poset):

Definition

For (S,)(S, \leq) a preorder and ASA \hookrightarrow S a subset, a lower bound of AA in SS is an element xx of SS such that xyx \leq y whenever yAy \in A.

Last revised on September 27, 2012 at 23:09:15. See the history of this page for a list of all contributions to it.