
Continuum = compact connected metrizable space

Indecomposable = not the union of any two proper subcontinua.

Homogeneous = for every two points $ x$ and $ y$ there is a homeomorphism of the space onto itself which maps $ x$ to $ y$ .

Unicoherent = the intersection of every two subcontinua is connected.
Examples of indecomposable homogeneous continua include solenoids, the pseudoarc, and solenoids of pseudoarcs (a solenoid with each point is blown up into a pseudoarc). I think it’s an open problem to determine whether this list is complete, but so far all of the examples are unicoherent. Is there a theorem stating that such continua must be unicoherent?