- Unicoherent
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.

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

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