bijection between closed and open interval
Then the mapping from to defined by
Note that the bijection is neither monotonic (e.g. , , ) nor continuous. Generally, there does not exist any continuous surjective mapping , since by the intermediate value theorem a continuous function maps a closed interval to a closed interval.
- 1 S. Lipschutz: Set theory. Schaum Publishing Co., New York (1964).
|Title||bijection between closed and open interval|
|Date of creation||2013-03-22 19:36:06|
|Last modified on||2013-03-22 19:36:06|
|Last modified by||pahio (2872)|