Thread: 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

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: 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 .

Thanks

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What is R(p)?

in lR p space