Dispersion point

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In topology, a dispersion point or explosion point is defined as follows:

If X is a connected topological space containing the point p and at least two other points, p is a dispersion point for X if and only if X\setminus \{p\} is totally disconnected. A space can have at most one dispersion point.

Some examples of spaces with a dispersion point are the Knaster-Kuratowski fan and any space with the particular point topology.

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