Glasnik Matematicki, Vol. 37, No.2 (2002), 347-363.

THE HYPERSPACE C2(X) FOR A FINITE GRAPH X IS UNIQUE

Alejandro Illanes

Instituto de Matematicas, Circuito Exterior, Cd. Universitaria, Mexico, 04510, Mexico
e-mail: illanes@matem.unam.mx


Abstract.   Let X be a metric continuum. Let C2(X) be the hyperspace of X consisting of all the nonempty and with at most two components closed subsets of X, with the Hausdorff metric. In this paper we prove that if X is a finite graph and Y is a metric continuum such that C2(X) is homeomorphic to C2(Y), then X is homeomorphic to Y.

2000 Mathematics Subject Classification.   54B20.

Key words and phrases.   Continuum, finite graph, hyperspaces, unique hyperspace.


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