Nankai order theory

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1、TopologicalCharacterizationofSemi-andIntervalOrdersJunZhang(IncollaborationwithYitongSun)UniversityofMichigan,AnnArbor02-22-2013JunZhang(IncollaborationwithYitongSun)TopologicalCharacterizationofSemi-andIntervalOrdersLecturePlanSemiorderandIntervalOrder1Abriefreviewofhistory2CharacterizationbyC

2、onditions2+2and1+33CharacterizationbyUpper/LowerHoldings4Nesting"phenomenonfromintervalorder5Branchingphenomenonandbranchorder"JunZhang(IncollaborationwithYitongSun)TopologicalCharacterizationofSemi-andIntervalOrdersLecturePlanSemiorderandIntervalOrder1Abriefreviewofhistory2Characterizationby

3、Conditions2+2and1+33CharacterizationbyUpper/LowerHoldings4Nesting"phenomenonfromintervalorder5Branchingphenomenonandbranchorder"TopologicalClassicationofIntervalOrderRelations1Alexandrovupper-settopology:areview2Topologicalseparabilityofpairsofpoints3Classicationofpairwiserelationsinaninter

4、valorderJunZhang(IncollaborationwithYitongSun)TopologicalCharacterizationofSemi-andIntervalOrdersMotivation:Intransitiveindierenceand"threshold"SoritesParadoxHeap("soros"inGreek)ofSand:onegrainofsandwouldnotmakeadierencebetweenbeingaheapornotaheap.BaldMan:onehairwouldnotmakeadierencebetweenb

5、eingbaldornotbeingbald.


JunZhang(IncollaborationwithYitongSun)TopologicalCharacterizationofSemi-andIntervalOrdersMotivation:Intransitiveindierenceand"threshold"SoritesParadoxHeap("soros"inGreek)ofSand:onegrainofsandwouldnotmakeadierencebetweenbeingaheapornotaheap.BaldMan:onehairwouldnotmake

6、adierencebetweenbeingbaldornotbeingbald.


Modernpsychophysicists(Fechner,Weber,Stevens,etc)approachestheissueofvagueness"bymeasuringabsolutethresholdandrelativethreshold.Thresholdisanessentialconceptinpsychology.JunZhang(IncollaborationwithYitongSun)TopologicalCharacterizationofSemi-andInter

7、valOrdersMotivation:Intransitiveindierenceand"threshold"SoritesParadoxHeap("soros"inGreek)ofSand:onegrainofsandwouldnotmakeadierencebetweenbeingaheapornotaheap.BaldMan:onehairwouldnotmakeadierencebetweenbeingbaldornotbeingbald.