Can a homeomorphism exist between an open and a half open set?

(ie: (0,1) and [0,1))

I know that to be a homeomorphism, a bijection must exist, they must be continuous, and they must have a continuous inverse... Where to go from here?

The fact that 0 is not included within the first set, would that alone make it so that it is not homeomorphic?

Thank you.

Jia Lin