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Fixed Point Theorems for Plane Continua with Applications (Memoirs of the American Mathematical Society) - Tapa blanda
Reseña del editor
In this memoir the authors present proofs of basic results, including those developed so far by Harold Bell, for the plane fixed point problem: Does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but without accessible proofs. The authors define the concept of the variation of a map on a simple closed curve and relate it to the index of the map on that curve: Index = Variation 1. A prime end theory is developed through hyperbolic chords in maximal round balls contained in the complement of a non-separating plane continuum $X$. They define the concept of an outchannel for a fixed point free map which carries the boundary of $X$ minimally into itself and prove that such a map has a unique outchannel, and that outchannel must have variation $-1$. Also Bell's Linchpin Theorem for a foliation of a simply connected domain, by closed convex subsets, is extended to arbitrary domains in the sphere. The authors introduce the notion of an oriented map of the plane and show that the perfect oriented maps of the plane coincide with confluent (that is composition of monotone and open) perfect maps of the plane. A fixed point theorem for positively oriented, perfect maps of the plane is obtained. This generalizes results announced by Bell in 1982.
Biografía del autor
Alexander M. Blokh, University of Alabama, Birmingham, AL, USA Robbert J. Fokkink, Delft Institute of Applied Mathematics, Netherland. John C. Mayer Lex G. Oversteegen, University of Alabama, Birmingham, AL, USA E. D. Tymchatyn, University of Saskatchewan, Saskatoon, SK, Canada
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- EditorialAmerican Mathematical Society
- Año de publicación2013
- ISBN 10 0821884883
- ISBN 13 9780821884881
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas97
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Imagen del vendedor
Fixed point theorems for plane continua with applications. Memoirs of the American Mathematical Society; 1053.
Publicado por
Providence, American Math. Soc, 2013
ISBN 10: 0821884883
ISBN 13: 9780821884881
Antiguo o usado
Softcover
Librería: Antiquariat Bookfarm, Löbnitz, Alemania
Calificación del vendedor: 5 de 5 estrellas
Softcover. Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-00028 9780821884881 Sprache: Englisch Gewicht in Gramm: 350. Nº de ref. del artículo: 2482527
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