Which connected spaces have a quotient homeomorphic to an arc
  We announce and examine the conjecture that each infinite connected normal Hausdorff space has a quotient homeomorphic to the unit interval, shown to be true with the additional assumption of compactness or local connectedness. Some connected subsets of the plane are considered to show the difficulties involved in developing a general argument. 
Micha{\l} Ryszard W\'ojcik
math.GN