# Math Help - problems in analysis

1. ## problems in analysis

- true or false:
every compact set in R(p) is connected in 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

Thanks

2. Originally Posted by nice rose
- 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

$f(x):= \left\{\begin{array}{cc}1&\,\mbox{if } x\neq 0\\0&\,\mbox{if } x=0\end{array}\right.$

- 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 $f([2,3])$ is a bounded interval. Now, just prove (using limits, say) that this interval is actually closed and there you are .

Thanks
.

3. What is R(p)?

in lR p space