By Paul A. Schweitzer, Steven Hurder, Nathan Moreira DOS Santos
This quantity includes the court cases of the Workshop on Topology held on the Pontif?cia Universidade Cat?lica in Rio de Janeiro in January 1992. Bringing jointly approximately one hundred mathematicians from Brazil and all over the world, the workshop coated various subject matters in differential and algebraic topology, together with crew activities, foliations, low-dimensional topology, and connections to differential geometry. the most focus was once on foliation conception, yet there has been a full of life alternate on different present subject matters in topology. the quantity comprises a very good checklist of open difficulties in foliation learn, ready with the participation of a few of the head international specialists during this region. additionally awarded listed here are surveys on team actions---finite staff activities and pressure thought for Anosov actions---as good as an straight forward survey of Thurston's geometric topology in dimensions 2 and three that will be available to complex undergraduates and graduate scholars.
Read or Download Differential Topology, Foliations, and Group Actions: Workshop on Topology January 6-17, 1992 Pontificia Universidade Catolica, Rio De Janeiro, Braz (Contemporary Mathematics) PDF
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Extra resources for Differential Topology, Foliations, and Group Actions: Workshop on Topology January 6-17, 1992 Pontificia Universidade Catolica, Rio De Janeiro, Braz (Contemporary Mathematics)
Example text
Die topologiscbe Zuordnung und ihre verschiedenen Erzeugungsarten. 33 Aufgabe 3 (HAUSDORFF). e Metrik in einer Menge R, ist, man durch , e'{a ' b)=~~ t+e(a,b) eine topologisch-gleichwertige Metrik erhlilt. 1st e(a, b) eigentlich, so gilt dasselbe auch von e' (a, b). Des weiteren ist fur jedes Paar (a, b) stets e' (a, b) < 1. Wir wollen diesem Resultat fur' metrische Raume gleich die Form eines allgemeinen Satzes geben. 'Satz IV. Unter den (eigentlichen) Metriken eines metrisierbaren Raumes gibe es solche, bei denen tier Raum beschrankt' ist (d.
A - B, die Differenz, bedeutet die Menge aller Punkte von A, die nicht zu B geh6ren. :::) ist auszusprechen: "ist enthalten in" bzw. "enthalt". Dementsprechend bedeuten A C B und B:::) A dasselbe, namIich, da/3 jedes Element von A gleichzeitig auch Element von B ist (d. h. da/3 A TeilMenge von B. oder B Obermenge von A ist; dabei wird der Fall A = B nicht ausgeschiossen). Es bezeichnet peA, da/3 der Punkt p ein Element der Menge A ist; zwischen einem Punkt und der aus diesem einzigen Punkt bestchenden Punktmenge wird nicht unterschieden.
Dadurch entsteht ein metrischer Raum C, der in der Funktionalanalysis von groI3er Bedeutung ist. Wir werden iibrigens auf Veraligemeinerungen dieses Raumes noch bei spaterer Gelegenheit zuriickkommen (vgl. § 3, Nr·3)· 3°. , t n ). Die beiden folgenden Metriken (1) und e«tl' ... , tn); (t~, e' «tl' ... , tn); ... , t~)) = 1'(t1 - 4)1 + ... + (tn - - 41 + ... + 1tn - (ti,···, t~)) = 1tl t~)2 t~ I sind topologisch-gleichwertig; der durch sie bestimmte aligemein-topologische Raum heiI3t der n-dimensionale Zahlenraum.