title: Phragmen–Brouwer theorem
text: # Phragmen–Brouwer theorem
  
  In topology, the Phragmén–Brouwer theorem, introduced by Lars Edvard Phragmén and Luitzen Egbertus Jan Brouwer, states that if X is a normal connected locally connected topological space, then the following two properties are equivalent:
  
  * If A and B are disjoint closed subsets whose union separates X, then either A or B separates X.
  * X is unicoherent, meaning that if X is the union of two closed connected subsets, then their intersection is connected or empty.
  
  The theorem remains true with the weaker condition that A and B be separated.
  
  