Recent content by pp007

I was trying to figure out why the sequence: 0 --> C_{o}((0,1)) --> C[([0,1]) --> C\oplusC --> 0 is exact but does not split. I got confused thinking that if the middle is not isomorphic to the direct sum of two sides then the sequence does not split. This is only the case when the one...

I assume that we are taking the sup norm. Is there a problem?

Sorry, I forgot to put in (0,1). For some reason, I think that I did. (Texing is not going very well for me.) So, It's the space of function on (0,1) vanishing at infinity.

Sorry for not being clear. Yes, C([0,1]) is as a Banach space and C_{o} is the space of function vanishing at infinity.

Can anyone explain why C([0,1]) and C_{o} \oplus C \oplus C (where C=complex ) are not isomorphic?