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Título del libro: Open Problems In Topology Ii
Título del capítulo: Open Problems on Dendroids

Autores UNAM:
VERONICA MARTINEZ DE LA VEGA Y MANSILLA; JORGE MARCOS MARTINEZ MONTEJANO;
Autores externos:

Idioma:
Inglés
Año de publicación:
2007
Resumen:

This chapter discusses basic concepts and some problems on dendroids. A continuum is defined as a compact, connected, metric space. A dendroid is an arc-wise connected and hereditarily unicoherent continuum. A dendrite is defined as a locally connected dendroid. Even though dendroids are one-dimensional and most of them can be geometrically realized, they have many properties and intrinsic characterizations that are still unknown. This chapter presents a survey of some results and open problems on dendroids. The chapter discusses about B. Knaster who saw dendroids as those continua for which for every e{open} > 0 there exists a tree T and an e{open}-retraction r: X ? T (an e{open}-retraction is a retraction such that diam(r-1(t)) <e{open} for every t ? T). The chapter presents the concepts that are related to mappings on dendrites, maps onto dendroids, contractibility, and hyperspaces. A discussion on property of Kelley, retractions, means, selections, smooth dendroids, planability, and shore sets is also presented in the chapter. © 2007 Elsevier B.V. All rights reserved.


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