Unicoherent

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A topological space X is said to be unicoherent if it is connected and 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.

[edit] References

Eric W. Weisstein et al. "Unicoherent Space." From MathWorld--A Wolfram Web Resource. [1]