Geodesic
One configurational characterization of Ostrom nets
Mathematica Bohemica, Tome 116 (1991) no. 2, pp. 132-147

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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 $(A_iA_j)$ (collinearity) for any five from six couples $\{i,j\}$ then there follows the collinearity coll $(A_kA_l)$ 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 condition.
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 $(A_iA_j)$ (collinearity) for any five from six couples $\{i,j\}$ then there follows the collinearity coll $(A_kA_l)$ 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 condition.
DOI : 10.21136/MB.1991.126140
Classification : 51A20, 51A25
Keywords: net; Ostrom net; quadrilateral closure condition; skew field; quadrangular condition 
Baštinec, Jaromír. One configurational characterization of Ostrom nets. Mathematica Bohemica, Tome 116 (1991) no. 2, pp. 132-147. doi: 10.21136/MB.1991.126140
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