Derivation is a polarity (Q1822759)

This paper is one in a series of three in which the author generalizes Ostrom's definition of derivation such that there is a 1-1-correspondence to the pairs consisting of a 3-dimensional projective space P and a special line N in it: Points of the derivable net are those lines of P that don't meet N, \(P\setminus N\) is the set of lines, two such lines being parallel if the projective line that connect their points meets N, and the set of subplanes of the net is the set of planes of P which don't contain N. Every finite net can be imbedded into an affine plane. In this paper it is shown that by interchanging the set of subplanes and the set of lines of a derivable net one gets another derivable net. Theorem: Let (P,N) be associated to a derivable net and \(\sigma\) : \(P\to P\) be a correlation such that \(\sigma (N)=N\). Then \((P^{\sigma},N)\) can be associated to the dual derivable net.