Displaying similar documents to “Generalization of one Baer's theorem for nets”

One configurational characterization of Ostrom nets

Jaromír Baštinec (1991)

Mathematica Bohemica

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Bz the quadrileteral condition in a given net there is meant the following implication: If A 1 , A 2 , A 3 , A - 4 are arbitrary points, no three of them lie on the same line, with coll ( A i A j ) (collinearity) for any five from six couples { i , j } then there follows the collinearity coll ( A k A l ) for the remaining couple { k , l } . In the article there is proved the every net satisfying the preceding configuration condition is necessarity the Ostrom net (i.e., the net over a field). Conversely, every Ostrom net satisfies the above configuration...