What is the minimum dimensionality of a dataset of a finite number of points where 1-NN has an accuracy of 0% but 3-NN has an accuracy of 100%.
This is certainly possible in 3 dimensions and my intuition is that an infinite number of points makes this possible in 2 dimensions, hence why I have tagged this in fractals, but not with finite points.
As an extension, what is the lower bound for the dimensionality of a dataset where n-NN has an accuracy of 0% but m-NN has an accuracy of 100%.