# Category:Boundedness

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This category contains results about **Boundedness**.

Definitions specific to this category can be found in Definitions/Boundedness.

Let $\struct {S, \preceq}$ be an ordered set.

Let $T \subseteq S$ be both bounded below and bounded above in $S$.

Then $T$ is **bounded in $S$**.

## Subcategories

This category has the following 11 subcategories, out of 11 total.

## Pages in category "Boundedness"

The following 24 pages are in this category, out of 24 total.

### C

- Characteristic of Increasing Mapping from Toset to Order Complete Toset
- Closed Subset of Real Numbers with Lower Bound contains Infimum
- Closure of Non-Empty Bounded Subset of Metric Space is Bounded
- Compact Subset of Normed Vector Space is Closed and Bounded
- Continuous Implies Locally Bounded
- Continuous Real Function Bounded on Finite Subdivision
- Continuous Real Function is Bounded on Neighborhood of Argument
- Continuous Real-Valued Function is not necessarily Bounded

### E

### S

- Sequence is Bounded in Norm iff Bounded in Metric/Necessary Condition
- Sequence is Bounded in Norm iff Bounded in Metric/Sufficient Condition
- Set of Integers is not Bounded
- Smallest Element is Lower Bound
- Subset of Bounded Above Set is Bounded Above
- Subset of Bounded Below Set is Bounded Below
- Supremum of Subset of Bounded Above Set of Real Numbers