On flags in a topological projective plane (Q1339799)

The flags of a topological projective plane \((P,{\mathcal L})\) form a closed subspace \(F \subset P \times {\mathcal L}\). Let \(\mathcal U\) be the space of all point rows and \(\mathcal V\) the space of all line pencils, where each point row and each pencil is viewed as a subset of \(F\), and write \({\mathcal S} = {\mathcal U} \cup {\mathcal V}\). The semi-linear space \((F,{\mathcal S})\) is called the flag space of the plane. \textit{A. Bichara, J. Misfeld}, and the author [Riv. Mat. Pura Appl. 11, 63-72 (1992; Zbl 0761.51012)] characterized the flag spaces of topological projective spaces. In the paper under review, the author expresses the defining properties of \((P,{\mathcal L})\) by a simplified set of axioms in terms of \((F,{\mathcal S})\).