## bounded

<*theory*> In domain theory, a subset S of a cpo X is
bounded if there exists x in X such that for all s in S, s <=
x. In other words, there is some element above all of S. If
every bounded subset of X has a least upper bound then X is
boundedly complete.

("<=" is written in LaTeX as \subseteq).

Last updated: 1995-02-03

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**Nearby terms:**

**bounded**» boundedly complete » bound variable » bournebasic

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