The Fundamental Theorem for locally projective geometries

Abstract We deal with generalizations of the Fundamental Theorem of Projective Geometry to other related geometries (of dimension $$\ge 3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> ) and non bijective maps. We consider locally projective geometries and locally affino-projective geometries (which include the classical Möbius, Laguerre and Minkowski geometries).