HEREDITARILY INDECOMPOSABLE HAUSDORFF CONTINUA HAVE UNIQUE HYPERSPACES 2(X) AND C-n(X)

作者：Illanes Alejandro^*

来源：Institut Mathematique, 2011, 89(103): 49-56.

DOI：10.2298/PIM1103049I

• generalized arc
• Hausdorff continuum
• hereditarily indecomposable
• hyperspace
• unique hyperspace
• Vietoris topology

Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2(X) (respectively, C-n(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2(X) (respectively C-n(X)) is homeomorphic to 2(Y) (respectively, C-n(Y)), then X is homeomorphic to Y.

• 出版日期2011