fundamentals of geometry (euclidean, non-euclidean)

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1、FundamentalsofGeometryOlegA.Belyaevbelyaev@polly.phys.msu.ru25thSeptember2005ContentsIClassicalGeometry11Absolute(Neutral)Geometry31.1Incidence....................................................3Hilbert’sAxiomsofIncidence.........................................3ConsequencesofIncidenceAxioms

2、......................................41.2BetweennessandOrder............................................7Hilbert’sAxiomsofBetweennessandOrder.................................7BasicPropertiesofBetweennessRelation..................................8BetweennessPropertiesfornCollinearPoints......

3、..........................14EveryOpenIntervalContainsInfinitelyManyPoints............................15FurtherPropertiesofOpenIntervals.....................................15OpenSetsandFundamentalTopologicalProperties.............................18BasicPropertiesofRays.........................

4、...................18LinearOrderingonRays............................................21OrderingonLines...............................................22ComplementaryRays..............................................25PointSetsonRays...............................................26BasicProperti

5、esofHalf-Planes........................................27PointSetsonHalf-Planes...........................................29ComplementaryHalf-Planes..........................................29BasicPropertiesofAngles...........................................34DefinitionandBasicPropertiesofGene

6、ralizedBetweennessRelations..................45FurtherPropertiesofGeneralizedBetweennessRelations..........................51GeneralizedBetweennessRelationfornGeometricObjects........................52SomePropertiesofGeneralizedOpenIntervals...............................54BasicPropertiesofGe

7、neralizedRays.....................................55LinearOrderingonGeneralizedRays.....................................57LinearOrderingonSetsWithGeneralizedBetweennessRelation.....................58ComplementaryGeneralizedRays...............