JP Journal of Geometry and Topology
Volume 2, Issue 1, Pages 75 - 96
(March 2002)
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DENDRITES WITH UNIQUE HYPERSPACE F2(X)
Alejandro Illanes (México)
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Abstract:
Let X
be a dendrite. Let F2(X)
be the hyperspace
of sets of the form {p,
q} such that
p, q
Î
X. In
this paper, we prove that if Y is a
continuum, then
(a) if F2(X) is
homeomorphic to F2(Y), then
Y is a dendrite and
(b) if F2(X) is
homeomorphic to F2(Y) and
the respective sets of ordinary points of X
and Y are open, then X is homeomorphic
to Y. |
| Keywords and phrases: continuum, dendrites, dendroids, hyperspaces, symmetric products, unique hyperspaces. |
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