Unicoherent space
In mathematics, a unicoherent space is a topological space <math>X</math> that is connected and in which the following property holds:
For any closed, connected <math>A, B \subset X</math> with <math>X=A \cup B</math>, the intersection <math>A \cap B</math> 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 (meaning that every subcontinuum is 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.
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