Wild Point
For any point P on the boundary of an ordinary ball, find a neighborhood of P in which the intersection with the ball's boundary cuts the neighborhood into two parts, each homeomorphic to a ball. A wild point is a point on the boundary that has no such neighborhood.
See also
Ball, Homeomorphic, NeighborhoodExplore with Wolfram|Alpha
WolframAlpha
More things to try:
Cite this as:
Weisstein, Eric W. "Wild Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WildPoint.html