| course | course_year | question_number | tags | title | year | |||
|---|---|---|---|---|---|---|---|---|
Analysis II |
IB |
14 |
|
2.I.1E |
2002 |
Define what is meant by (i) a complete metric space, and (ii) a totally bounded metric space.
Give an example of a metric space that is complete but not totally bounded. Give an example of a metric space that is totally bounded but not complete.
Give an example of a continuous function that maps a complete metric space onto a metric space that is not complete. Give an example of a continuous function that maps a totally bounded metric space onto a metric space that is not totally bounded.
[You need not justify your examples.]