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
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
References
- Abry, Mohammad; Dijkstra, Jan J.; van Mill, Jan (2007), "On one-point connectifications", Topology and its Applications 154 (3): 725–733, doi:10.1016/j.topol.2006.09.004, http://www.math.vu.nl/~vanmill/papers/papers2007/abry.pdf. (Note that this source uses hereditarily disconnected and totally disconnected for the concepts referred to here respectively as totally disconnected and totally separated.)
![]() | Original source: https://en.wikipedia.org/wiki/Dispersion point.
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