bounded
Let be a subset of . We say that is bounded when there exists a real number such that for all . When is an interval, we speak of a bounded interval.
This can be generalized first to . We say that is bounded if there is a real number such that for all and is the Euclidean distance between and .
This condition is equivalent to the statement: There is a real number such that for all .
A further generalization to any metric space says that is bounded when there is a real number such that for all , where is the metric on .
Title | bounded |
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Canonical name | Bounded1 |
Date of creation | 2013-03-22 14:00:00 |
Last modified on | 2013-03-22 14:00:00 |
Owner | yark (2760) |
Last modified by | yark (2760) |
Numerical id | 11 |
Author | yark (2760) |
Entry type | Definition |
Classification | msc 54E35 |
Related topic | EuclideanDistance |
Related topic | MetricSpace |
Defines | bounded interval |