A topological space X is said to be unicoherent if it is connected and the following property holds:

For any closed, connected A, B subset X with X=A cup B, the intersection A cap B is connected.

For example, any closed interval on the real line is unicoherent, but a circle is not.


*MathWorld|urlname=UnicoherentSpace|title=Unicoherent Space|author=Insall, Matt

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