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The one-nearest-neighbour classification boundary consists of the portions of the Voronoi diagram separating cells whose observed labels differ. For these nine grid points it forms diagonal and vertical or horizontal perpendicular-bisector segments around the three triangular observations. Every training point is its own nearest neighbour, so, absent a distance tie convention that excludes the query itself, its training error is zero.

For two classes, write $m(x)=\min \{p_1(x),p_2(x)\}$, the conditional Bayes error. The nearest-neighbour label and the test label become conditionally independent draws from the same local class distribution, so the limiting conditional error of one-nearest-neighbour classification isThe assumption gives $c\le m(x)\le 1/2-c$. Its excess over the conditional Bayes error isAfter taking expectations, the limiting risk remains at least $2c^2$ above the Bayes risk, so one-nearest-neighbour classification is not consistent.