Unicoherent space
In mathematics, a unicoherent space is a topological space that is connected and in which the following property holds:
For any closed, connected with, the intersection is connected.
For example, any closed interval on the real line is unicoherent, but a circle is not.
If a unicoherent space is more strongly hereditarily unicoherent and arcwise connected, then it is called a dendroid. If in addition it is locally connected then it is called a dendrite. The Phragmen–Brouwer theorem states that, for locally connected spaces, unicoherence is equivalent to a separation property of the closed sets of the space.
