Weak Linear Mappings – A Survey
نویسنده
چکیده
There are various concepts of structure preserving mappings in geometry. It is the aim of the present paper to give a survey on geometrical characterizations of some of those mappings. We discuss the results for projective spaces in some detail and report on generalizations to other spaces. We shall come across partially defined mappings. The notation φ : P → P ′ is used in order to point out that φ is a mapping with domain domφ ⊂ P and image set imφ ⊂ P ′. The exceptional set of φ (with respect to P) is given as exφ := P \domφ. The mapping φ is said to be globally defined (with respect to P) provided that exφ is empty. The notation φ : P → P ′ is maintained for globally defined mappings only. If we are given any subset M ⊂ P, then {Xφ | X ∈ M ∩ domφ} is a well–defined set. By abuse of notation, it is written as Mφ. Hence Mφ = ∅ exactly for M⊂ exφ.
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