- "Bounded" and "boundary" are distinct concepts; for the latter see boundary (topology). A circle in isolation is a boundaryless bounded set, while the half plane is unbounded yet has a boundary.
In
mathematical analysis and related areas of
mathematics, a
set is called
bounded, if it is, in a certain sense, of finite size. Conversely, a set which is not bounded is called
unbounded. The word bounded makes no sense in a general topological space, without a
metric.