The Collaborative International Dictionary of English v.0.48:

bounded \bounded\ adj.
   1. having the limits or boundaries established.

   Syn: delimited.
        [WordNet 1.5]

   2. having a defined physical border.
      [WordNet 1.5]

The Collaborative International Dictionary of English v.0.48:

Bound \Bound\, v. t. [imp. & p. p. Bounded; p. pr. & vb. n.
   Bounding.]
   [1913 Webster]
   1. To limit; to terminate; to fix the furthest point of
      extension of; -- said of natural or of moral objects; to
      lie along, or form, a boundary of; to inclose; to
      circumscribe; to restrain; to confine.
      [1913 Webster]

            Where full measure only bounds excess. --Milton.
      [1913 Webster]

            Phlegethon . . .
            Whose fiery flood the burning empire bounds.
                                                  --Dryden.
      [1913 Webster]

   2. To name the boundaries of; as, to bound France.
      [1913 Webster]

WordNet (r) 3.0 (2006):

bounded
    adj 1: having the limits or boundaries established; "a delimited
           frontier through the disputed region" [syn: bounded,
           delimited]

The Free On-line Dictionary of Computing (30 December 2018):

bounded

    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).

   (1995-02-03)