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I am interested in the affine version of the well-known Hessenberg's Theorem (saying that Pappian projective planes are Desarguesian). First I introduce all necessary definitions. Definition L. A ...

Definition 1. An affine plane is a pair $(X,\mathcal L)$ consisting of a set $X$ and a family $\mathcal L$ of subsets of $X$ called lines which satisfy the following axioms: Any distinct points $x,y\...

The classical synthetic notion of projective plane consists of a set of points, a set of lines, and a relation of incidence between the two, such that any two distinct points lie on a unique line and ...

Is there a quadrangle $Q \subset \Bbb CP^2$, namely $Q$ is a set of four points, such that every permutation of $Q$ can be realizad by an isometric projectivity of $\Bbb CP^2$? Clearly the analogous ...