On internal composants of indecomposable plane continua
J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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Nell Stevenson (1972)
Fundamenta Mathematicae
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Sam Nadler (1980)
Fundamenta Mathematicae
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J. Krasinkiewicz (1974)
Fundamenta Mathematicae
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A. Lelek, D. Zaremba (1962)
Fundamenta Mathematicae
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R. Moore (1929)
Fundamenta Mathematicae
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Charles L. Hagopian, Janusz R. Prajs (2005)
Fundamenta Mathematicae
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We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.
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.
Gail Atneosen (1972)
Fundamenta Mathematicae
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J. Chartonik (1980)
Fundamenta Mathematicae
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