Displaying similar documents to “Universal analytic preorders arising from surjective functions”

On confluently graph-like compacta

Lex G. Oversteegen, Janusz R. Prajs (2003)

Fundamenta Mathematicae

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For any class 𝒦 of compacta and any compactum X we say that: (a) X is confluently 𝒦-representable if X is homeomorphic to the inverse limit of an inverse sequence of members of 𝒦 with confluent bonding mappings, and (b) X is confluently 𝒦-like provided that X admits, for every ε >0, a confluent ε-mapping onto a member of 𝒦. The symbol 𝕃ℂ stands for the class of all locally connected compacta. It is proved in this paper that for each compactum X and each family 𝒦 of graphs,...

Analytic partial orders and oriented graphs

Alain Louveau (2006)

Fundamenta Mathematicae

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We prove that there is no maximum element, under Borel reducibility, in the class of analytic partial orders and in the class of analytic oriented graphs. We also provide a natural jump operator for these two classes.

Graphs with multiple sheeted pluripolar hulls

Evgeny Poletsky, Jan Wiegerinck (2006)

Annales Polonici Mathematici

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We study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.

Waraszkiewicz spirals revisited

Pavel Pyrih, Benjamin Vejnar (2012)

Fundamenta Mathematicae

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We study compactifications of a ray with remainder a simple closed curve. We give necessary and sufficient conditions for the existence of a bijective (resp. surjective) mapping between two such continua. Using those conditions we present a simple proof of the existence of an uncountable family of plane continua no one of which can be continuously mapped onto any other (the first such family, so called Waraszkiewicz's spirals, was created by Z. Waraszkiewicz in the 1930's).

Fully closed maps and non-metrizable higher-dimensional Anderson-Choquet continua

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.

No arc-connected treelike continuum is the 2-to-1 image of a continuum

Jo Heath, Van C. Nall (2003)

Fundamenta Mathematicae

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In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. In 2003 we show that no arc-connected treelike continuum is the 2-to-1 image of a continuum.

Whitney properties

J. Krasinkiewicz, Sam Nadler (1978)

Fundamenta Mathematicae

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