TopologicalrelationshipsbetweentwospatialfeaturesrepresentimportantknowledgeinGeographicalInformationSystems(GIS).Inthelastfewyears,manymodelsthatrepresenttopologicalrelationshipshavebeenproposed.Butthesemodelscannotrepresentthetopologicalrelationshipsbetweenheterogeneousgeometrycollectionfeatures,whicharecomposedofdifferentdimensionalgeometries.Inthispaper,theformaldefinitionofregularheterogeneousgeometrycollectionandregularizationrulesaregiven.Basedonthespatialmodel,twomethodsforrepresentingtopologicalrelationshipsbetweenthesecomplexfeaturesareproposed.ThefirstmethodisDimensionallyExtendedNine-IntersectionModelBasedonComponents(DE-9IMBC)thatextendsDimensionallyExtendedNine-IntersectionModel(DE-9IM)andtakesintoaccountthetopologicalrelationshipsbetweencomponentsofthesecomplexfeatures.TheadvantageofDE-9IMBCisthatalargenumberofdifferenttopologicalrelationshipscanbechecked.ThesecondmethodextendsthedefinitionsoftopologicalrelationshipsinOpenGeodataInteroperabilitySpecification(OpenGIS),andredefinesthesevennamedtopologicalrelationships:{Disjoint,Touches,Within,Crosses,Overlaps,ContainsandEqual},torepresentthetopologicalrelationshipsbetweenheterogeneousgeometrycollectionfeatures.Itisproventhatthesevenextendedtopologicalrelationshipsarecompleteandmutuallyexclusive,andtheyaresuitableforbeingembeddedinspatialquerylanguages.
