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