Strong general position and Menger curves (Q1601643)

The notion of strong general position for a finite simplicial complex in \(\mathbb R^n\) extends to a countable complex by ensuring that the coordinates of the vertices are algebraically independent. This then ensures that every hyperplane \(H\) meets at most \(\frac{(n-\text{dim}H)(1+\dim H)}{n-m-\dim H}\) simplices of dimension at most \(m<n-\dim H\). The ideas are then applied to Menger curves where the same bounds are achieved.