I can sort of see how this works.
We can wrap the interval around itself to produce a circle. (continuous)
But if we take a circle and "rip" it and make it a line, that is no longer continuous.
But is there a way to state this more formally? Also this question is listed under connectedness, is there some sort of argument that can be made that way? But both spaces seem to be connected though.
Thank you for your help.