By K. Borsuk & W. Szmielew

This publication is anxious with the rules of Euclidean, Bolyai-Lobachevskian

(hyperbolic) and genuine projective geometries and consists of the improvement of every to the

point at which the method of axioms may be proven to be express in addition to constant.

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Ce cours de topologie a été dispensé en licence à l'Université de Rennes 1 de 1999 à 2002. Toutes les constructions permettant de parler de limite et de continuité sont d'abord dégagées, puis l'utilité de l. a. compacité pour ramener des problèmes de complexité infinie à l'étude d'un nombre fini de cas est explicitée.

This publication is the 6th version of the vintage areas of continuing Curvature, first released in 1967, with the former (fifth) variation released in 1984. It illustrates the excessive measure of interaction among staff idea and geometry. The reader will enjoy the very concise remedies of riemannian and pseudo-riemannian manifolds and their curvatures, of the illustration concept of finite teams, and of symptoms of contemporary growth in discrete subgroups of Lie teams.

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6. INTERVALS The purpose of this last section is to obtain a criterion for the existence of transversals to a set of intervals in Rn. By an interval we mean any connected subset of a line, so that they may also be open, rays or complete lines. A line being transversal to a set of intervals means that it does intersect all of them. 1 to intervals, requires the Hadwiger hypothesis of partial transversals compatible with a given linear order. Because 14 AROCHA, BRACHO AND MONTEJANO we have been working in projective space, where the general problem really lies, one other natural Hadwiger-type hypothesis to consider is compatibility with a given cyclic order.

O l r _ f c ; o n _ f c + i , o n _ f c + 2 , . . ,o n }, ij G { 1 , 2 , . . ,r — k belongs exactly to two classes containing the chosen ktuple ffki an(l therefore these (r — fc)-tuple belongs to exactly one such pair of classes. So, it must be true that (2) > ("l£)- Hence, zAi/-2(™~£) > 0. From this we get the desired inequality. : On a certain class of incidence structures. Prace a stiidie Vysokej skoly dopravnej v Ziline 2 (1979), 97-106. : On a connection between unit circles and horocycles determined by n points.

Geometry (ED. -R. Sack and J. Urrutia), pp. 633-701. V. North-Holland, Amsterdam, 2000. [5] C. H. Papadimitriou, and M. Yannakakis, Shortest paths without a map, Jour. Proc. 16th Internat. Colloq. on Automata, Languages, and Programming, Lecture Notes in Computer Science 372, 610-620, SpringerVerlag (1989). edu ''Donald R. edu ''Andras Bezdek'' A SHORT SURVEY OF (r,g)-STRUCTURES VOJTECH BALINT1 Department of Mathematics, University of Zilina, 010 26 Zilina, Slovakia. ABSTRACT. This contribution gives a short survey of results on the combinatorial (r, g)-structures as the generalization of many geometrical structures.