The Hyperspaces C(p,X) for Atriodic Continua

• Autores: Patricia Pellicer Covarrubias
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 2, 2005, págs. 403-426
• Idioma: inglés
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• Resumen

  • Let C(X) denote the hyperspace of subcontinua of a continuum X. For an element A of C(X), define the hyperspace C(A,X) as the set of elements of C(X) which contain A. We prove that nondegenerate Whitney levels of C(p,X) are arcs when X is an atriodic continuum. The main result is a characterization of the hyperspaces C(p,X) for atriodic continua. Moreover, as a consequence of the characterization, we obtain that a continuum X is atriodic if and only if C(A,X) is planar for every element A of C(X).