1
A connected space $X$ is said to be unicoherent if for any two closed connected subspaces $A$, $B$ such that $A\cup B = X$ then $A\cap B$ is connected. I came across an exercise which asks to show that $I=[0,1]$ is unicoherent, that $S^1$ is not, and to determine whether $S^2$ is unicoherent or n...