- true or false: every compact set in R(p) is connected in R(p)
What is R(p)?
- find an example of a function is uncontinuous at x in it is domin but it has a limit at x
- f: R--------> R continuous proof that f([2,3]) is compact set in R
Continuous functions map intervals to intervals, and by boundness of f it must be that is a bounded interval. Now, just prove (using limits, say) that this interval is actually closed and there you are .