Glasnik Matematicki, Vol. 37, No.2 (2002), 347-363.
THE HYPERSPACE C2(X) FOR A
FINITE GRAPH X IS UNIQUE
Instituto de Matematicas, Circuito Exterior,
Cd. Universitaria, Mexico, 04510, Mexico
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.
Key words and phrases. Continuum, finite graph,
hyperspaces, unique hyperspace.
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