4-Dimensional compact projective planes with a 5-dimensional by Betten D.

By Betten D.

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Math. 10 (1958), 321-348. 6. Browder, F. : Covering spaces, fiber spaces and local homeomorphisms, Duke Math. J. 21 329-336. 7. : Homologies and elations in compact, connected projective planes, TopologyAppL 12 (1981), 49-63. 8. : Topologische Differenzenfltichenebenen, Kiel, 1983. 9. Knarr, N. : Ein Kriterium fiir topologische Tem~rk6rper, Arch. Math. 46 (1986), 368-370. 10. 2, Results Math. 12 (1987), 134-147. 11. :4-dimensionaleprojektiveEbenenmitgrol]erabelscherKollineationsgmppe, J. Geom. 31 (1988), 114-124.

10. 2, Results Math. 12 (1987), 134-147. 11. :4-dimensionaleprojektiveEbenenmitgrol]erabelscherKollineationsgmppe, J. Geom. 31 (1988), 114-124. 12. : Four-dimensional compact projective planes with a nonsolvable automorphism group, Geom. Dedicata 36 (1990), 225-234. 13. : Classification of solvable Lie algebras of sixth order with one nonnilpotent basis element, Izv. Vyssh. Uchebn. Zaved. Matematica 4 (1963), 104-116. 14. Ortega, J. M. and Rheinboldt, W. : lterative Solution of Nonlinear Equations in Several Variables, Academic Press New York: (1970).

Eliminating y we get one equation for z. e. if (w+, z+) = (~, ~4). 4-DIMENSIONALCOMPACTPROJECTIVEPLANESWITH A 5-DIMENSIONALNILRADICAL 289 F o r x ~ - oo w e get similar expressions, replace the indices + b y - . F r o m (R) and (L) it f o l l o w s that 4 z + - w + _< 0 and 4 z _ - w _ _< 0. F u r t h e r m o r e the a s s u m p t i o n t ~ 0 implies - ~ t 4 - b2 < 0. T h e r e f o r e in any case we h a v e limx__+~ f ( z ) = - ~ and l i m x ~ _ ~ f ( z ) = c~. H e n c e there exists a solution o f f ( x ) = 0 and the t w o lines intersect.

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