Thread: Inverse functions

I've been set a question and I just want to verify I have understood it and would like a few pointers on solving it.

Given R=C[0,1]
-Firstly this is any function that is continuous on the domain [0,1] ?
I.e. f:[0,1] -> Reals

-The group of units is all continuous functions that are invertible on [0,1].
By my understanding: those that have no asymptotes (continuity), and no roots (invertibility) on [0,1].

Is there any way to classify these functions more rigourously?

Thanks

Originally Posted by mrmango

I've been set a question and I just want to verify I have understood it and would like a few pointers on solving it.

Given R=C[0,1]
-Firstly this is any function that is continuous on the domain [0,1] ?
I.e. f:[0,1] -> Reals

Well, is the set of all bounded functions continuiously. In your case you just lucked out that continuity implies boundedness.

-The group of units is all continuous functions that are invertible on [0,1].
By my understanding: those that have no asymptotes (continuity), and no roots (invertibility) on [0,1].

Is there any way to classify these functions more rigourously?

Thanks

I'm not sure what you mean here? You can turn into a ring?

Thanks for your reply,

Im pretty sure it is a ring, but correct me if i'm wrong

Thanks again

Originally Posted by mrmango

Thanks for your reply,

Im pretty sure it is a ring, but correct me if i'm wrong

Thanks again

It is a ring.