Existence of an homeomorphic between [0,1] to X × Y I'm doing a practice exam questions and am stuck at this question:

Are there topological spaces X,Y (each with more than one point), such that [0,1] is homeomorphic to X×Y? What if we replace [0,1] with R?

I'm not even sure how to start tackle it, any help and clues will be appreciated! My head is leading me to "cut-points" area, but I'm not sure abuot it./
Thanks in advance! 

Hints: Prove that:


*

*If $X\times Y$ is homeomorphic to $[0,1]$, then both $X$ and $Y$ are connected.

*If $x_0\in X$ and $y_0\in Y$, then $(X\times Y)\setminus\{(x_0,y_0)\}$ is still connected.

