منابع مشابه
HEREDITARILY INDECOMPOSABLE HAUSDORFF CONTINUA HAVE UNIQUE HYPERSPACES 2XAND Cn(X)
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, C...
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For a hereditarily unicoherent continuum X, its kernel means the common part of all subcontinua of X that intersect all arc components of X. This concept naturally appears when absolute retracts for the class of hereditarily unicoherent continua are studied. Let Y be such an absolute retract. Among other results, we prove that (a) Y is indecomposable if and only if it is identical with its kern...
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We prove that a space with a σ-weakly hereditarily closurepreserving sn-network is sn-first countable. As an application of this result, we prove that a Lindelöf space with a σ-weakly hereditarily closurepreserving sn-network is sn-second countable. The above results answer some questions posed by L. Yan. AMS Mathematics Subject Classification (2000): 54D20, 54D65, 54E20, 54E99
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Le Roux and Ziegler asked whether every simply connected compact nonempty planar Π 1 set always contains a computable point. In this paper, we solve the problem of le Roux and Ziegler by showing that there exists a planar Π 1 dendroid without computable points. We also provide several pathological examples of tree-like Π 1 continua fulfilling certain global incomputability properties: there is ...
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The well-known result of S. Mazurkiewicz that the simple closed curve is the only nondegenerate locally connected plane homogeneous continuum is extended to generalized homogeneity with respect to some other classes of mappings. Several open problems in the area are posed.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1979
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-41-1-57-65