Wojciech Stadnicki (2012)
Colloquium Mathematicae
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We prove that, for any Hausdorff continuum X, if dim X ≥ 2 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then either dim C(X) = 2 or C(X) is not a C-space. This generalizes some results known for metric continua.
Ivan Lončar (2003)
Publications de l'Institut Mathématique
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Lončar, Ivan (2003)
Publications de l'Institut Mathématique. Nouvelle Série
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Lončar, Ivan (2003)
Publications de l'Institut Mathématique. Nouvelle Série
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Phillip Zenor (1980)
Fundamenta Mathematicae
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Witold Bula (1981)
Colloquium Mathematicae
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Roman Mańka (2002)
Fundamenta Mathematicae
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It is proved that the cylinder X × I over a λ-dendroid X has the fixed point property. The proof uses results of [9] and [10].
A. Emeryk (1972)
Fundamenta Mathematicae
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Jerzy Krzempek (2010)
Colloquium Mathematicae
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Fedorchuk's fully closed (continuous) maps and resolutions are applied in constructions of non-metrizable higher-dimensional analogues of Anderson, Choquet, and Cook's rigid continua. Certain theorems on dimension-lowering maps are proved for inductive dimensions and fully closed maps from spaces that need not be hereditarily normal, and some of the examples of continua we construct have non-coinciding dimensions.
Lee Mohler, Lex Oversteegen (1990)
Fundamenta Mathematicae
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H. Cook (1964)
Colloquium Mathematicae
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Sergio Macías (2007)
Colloquium Mathematicae
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We prove a decomposition theorem for a class of continua for which F. B.. Jones's set function 𝓣 is continuous. This gives a partial answer to a question of D. Bellamy.
Heikki J. K. Junnila (1988)
Commentationes Mathematicae Universitatis Carolinae
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J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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Janusz Charatonik, Włodzimierz Charatonik (2000)
Colloquium Mathematicae
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It is shown that there is no Whitney map on the hyperspace for non-metrizable Hausdorff compact spaces X. Examples are presented of non-metrizable continua X which admit and ones which do not admit a Whitney map for C(X).