# bounded

### Analysis

A set or sequence of values is called bounded if there is a value $$M$$ such that the values are never greater than $$M$$ and never smaller than $$-M$$. A function is bounded if its values are bounded. A sequence of functions is pointwise bounded if at every domain element $$x$$ the sequence of values of the functions at $$x$$ is bounded.

### Topology

A subset $$E$$ of a locally compact topological space is bounded if there exists a compact set $$C$$ such that $$E$$ is contained in $$C$$. Such a subset is called $$s$$-bounded if there exists a sequence of compact sets $$C_i$$ such that $$E$$ is contained in their union.