### Unit square

Is it possible to partition a unit square [0, 1] X [0, 1] into two disjoint connected subsets A and B such that A and B contain opposing corners? I.e., such that A contains (0, 0) and (1, 1), and B contains (1, 0) and (0, 1)? *----0 | | | | 0----* Evidently, A and B couldn't be path-connected because a path running fr