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Título del libro: Open Problems In Topology Ii
Título del capítulo: Hyperspaces of Continua

Autores UNAM:
ALEJANDRO ILLANES MEJIA;
Autores externos:

Idioma:
Inglés
Año de publicación:
2007
Resumen:

This chapter presents basic concepts related to hyperspaces of continua and various problems posed since 1999. The chapter defines a continuum as a compact, connected metric space with more than one point. In the chapter, X denotes a continuum, the hyperspaces of X are defined as: 2. X = {. A ?. X: A is closed and nonempty}, C(X) = {A ? 2. X: A is connected}, Fn(X) = {A ? 2. X: A has at most n points}, Cn(X) = {. A ? 2. X: A has at most n components}. The hyperspace 2. X is equipped with the Hausdorffmetric H. The space Fn(X) is called n-symmetric product and Cn(X) is called n-fold hyperspace. Whitney maps are important tools in the study of hyperspaces. They were introduced by H. Whitney in a context different of hyperspaces. Concepts related to Whitney and diameter maps, fixed-point property, and locating cells in hyperspaces are also elaborated in the chapter. It also discusses about mappings between hyperspaces and unique hyperspaces. © 2007 Elsevier B.V. All rights reserved.


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