A little help:
(i) closed, bounded and compact is possible.
Choose
(ii) closed, not bounded and compact is impossible because:
is compact iff is closed and bounded.
...
Fernando Revilla
With sixty other postings, you should understand that this is not a homework service nor is it a tutorial service. So you need to show some of your own work on this problem or explain what you do not understand about the question.
Here is a start. is closed, bounded, and compact.
is not closed, not bounded, and not compact.
Hi sorry about this.
I have considered some cases:
1 A union of closed and bounded set atr compact.
i.e [0,1] U [2,3]
2. (0,1) not closed so not compact
3. {1/n, n=1,2,3,...} U {0} compact bounded and closed
4. empty set compact bounded and closed
5. set R of all real numbers. Not compact