For any point 
on the boundary of an ordinary ball, find a neighborhood
of 
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.
Wild Point
See also
Ball, Homeomorphic, NeighborhoodExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Wild Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WildPoint.html