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In topology, a dispersion point or explosion point is a point in a topological space the removal of which leaves the space highly disconnected.
More specifically, 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 ∖ { p } {\displaystyle X\setminus \{p\}} is totally disconnected. If X is connected and X ∖ { p } {\displaystyle X\setminus \{p\}} is totally separated then p is an explosion point. A space can have at most one dispersion point or explosion point. Every totally separated space is totally disconnected, so every explosion point is a dispersion point.
The Knaster–Kuratowski fan has a dispersion point; any space with the particular point topology has an explosion point.
If p is an explosion point for a space X, then the totally separated space X ∖ { p } {\displaystyle X\setminus \{p\}} is said to be pulverized.