Determine whether there exists a function that is continuous on all of where it has range that's equal to
Follow Math Help Forum on Facebook and Google+
There isn't such a function, because if f is continuous than must be an interval and is not an interval.
Originally Posted by red_dog There isn't such a function, because if f is continuous than must be an interval and is not an interval. ? let which continuous on R. is an interval?
Originally Posted by kalagota ? let which continuous on R. is an interval? Continous functions map intervals into intervals or single points. In either case what reddog said is absolutely true. EDIT: It would be easier to use the fact that cotinous functions map connected sets to connected sets, R is connected, Q is not.
View Tag Cloud