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.

See also

• Phragmen–Brouwer theorem ‎

References

• Insall, Matt, "Unicoherent Space" from MathWorld.