Hereditarily indecomposable Hausdorff continua have unique hyperspaces 2X and Cn(X)
2011 ◽
Vol 89
(103)
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pp. 49-56
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Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(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 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, Cn(Y )), then X is homeomorphic to Y.
2020 ◽
Vol 57
(2)
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pp. 139-146
2021 ◽
Vol 288
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pp. 107480
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2002 ◽
Vol 66
(6)
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pp. 1087-1101
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2014 ◽
Vol 203
(1)
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pp. 341-387
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1997 ◽
Vol 29
(3)
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pp. 338-344
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1994 ◽
Vol 05
(02)
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pp. 201-212
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Keyword(s):
Keyword(s):