Dispersion point

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 $X\setminus \{p\}$ is totally disconnected (every subspace is disconnected, or, equivalently, every connected component is a single point). If X is connected and $X\setminus \{p\}$ is totally separated (for each two points x and y there exists a clopen set containing x and not containing y) 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.

单词	Dispersion point
释义	Dispersion point 英语百科 Dispersion point 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 $X\setminus \{p\}$ is totally disconnected (every subspace is disconnected, or, equivalently, every connected component is a single point). If X is connected and $X\setminus \{p\}$ is totally separated (for each two points x and y there exists a clopen set containing x and not containing y) 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.
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