1. The definition of bounded sets can be generalized to topological modules. 2. All bounded sets have a lower bound, by definition. 3. Furthermore, any bounded set in " H " is weakly compact. 4. Libraries collect individual published books and serials, or bounded sets of individual items. 5. Most generally, a system may be defined as a bounded set of interrelated or interacting elements. 6. And third of all, it says it works with any bounded sets , which is demonstrably false. 7. In mathematics articles, this usually involves a noun like Bounded set in preference to an adjective like Bounded. 8. I think I know how this should be true when this is a definite integral over a bounded set . 9. The underlying idea is the following : a bounded set can be covered by a single ball of some radius. 10. Bounded sets are a natural way to define a polar of a bounded set is an absolutely convex and absorbing set.
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