Let (P,L,I) be an affine plane, and let C be the set of parallelism equiva- lence classes
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Let (P,L,I) be an affine plane, and let C be the set of parallelism equiva- lence classes of L. Let ∞ be a element such that ∞ ∈/ L. For the relation I′ given by P ∈ P and m ∈ L and P I m , or PI′m ⇔ P ∈Candm∈Landm∈P,or P ∈ C and m = ∞ the point-line geometry (P ∪ C, L ∪ {∞}, I′) is a projective plane.
Prove the above theorem and explain
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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