GENERALIZATIONS OF THE FUNDAMENTAL THEOREM OF PROJECTIVE GEOMETRY.

The article presents a thesis discussing the fundamental theorem of projective geometry, which states that a semilinear transformation induces every line-preserving bijection of a Desaguersian projective plane. It is stated that the theorem extends to higher-dimensional projective spaces, affine transformations and even to buildings, which are combinatorial constructions. It considers the spaces' bijections preserving their geometry such as the transformations of quasi-spheres and proves local versions of theorems on arbitrary nondiscrete fields. Details on the parts of the thesis, which include a review of the theorem, nondiscrete topological fields and hypotheses involving measurable sets, are presented.