Elation switching in real parallelisms (Q447739)

Let \(F\) be a skew field and \(\mathrm{PG}(3,F)\) a projective space over \(F\). A parallelism of \(\mathrm{PG}(3,F)\) is an equivalence relation on the set of lines satisfying the Euclidean parallel postulate.NEWLINENEWLINE In this work the authors construct new parallelisms in \(\mathrm{PG}(3,K)\), where \(K\) is a subfield of real numbers. A particular replacement procedure, called switching of spreads, is used. They prove that if \(K\) is the field of real numbers, there exist \(2^{\aleph_{0}}\) mutually non-isomorphic parallelisms.