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Large Ordered Arcs
by
Mauricio Esteban Chacon-Tirado
Universidad Nacional Autonoma de Mexico
Given a metric continuum X, let C(X) be the hyperspace of subcontinua of X. A Large Ordered Arc (LOA) in C(X) is a subcontinuum A of C(X) such that A is an arc joining an element of the form {x} (x in X) to X and satisfying that if B,C are elements of A, then B is a subset of C or C is a subset of B. Let LOA(X) be the space of all LOA in C(X), considered as a subspace of C(C(X)). For a given x in X, let LOA(x,X) be the subspace of LOA(X) consisting of all LOA in C(X) that contain {x}. In this talk we present some results on LOA(X) and LOA(x,X). For example we can prove that LOA(x,X) always is either a singleton or a Hilbert cube.
Date received: February 19, 2009
Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayo-08.