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9 votes
2 answers
383 views

Does the Affine Pappus Axiom imply the Affine Desargues Axiom in affine planes?

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 ...
Taras Banakh's user avatar
7 votes
1 answer
347 views

A corollary of the affine Desargues axiom

Definition 1. An affine plane is a pair (X,L) consisting of a set X and a family L of subsets of X called lines which satisfy the following axioms: Any distinct points $x,y\...
Taras Banakh's user avatar
2 votes
1 answer
153 views

Very symmetric quadrangle in CP2

Is there a quadrangle QCP2, namely Q is a set of four points, such that every permutation of Q can be realizad by an isometric projectivity of CP2? Clearly the analogous ...
Daniele Zuddas's user avatar
15 votes
4 answers
966 views

Synthetic projective lines

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 ...
Mike Shulman's user avatar
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