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Displaying similar documents to “Covering the real line with translates of a zero-dimensional compact set”

The dimension of hyperspaces of non-metrizable continua

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.

Applications of some strong set-theoretic axioms to locally compact T₅ and hereditarily scwH spaces

Peter J. Nyikos (2003)

Fundamenta Mathematicae

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Under some very strong set-theoretic hypotheses, hereditarily normal spaces (also referred to as T₅ spaces) that are locally compact and hereditarily collectionwise Hausdorff can have a highly simplified structure. This paper gives a structure theorem (Theorem 1) that applies to all such ω₁-compact spaces and another (Theorem 4) to all such spaces of Lindelöf number ≤ ℵ₁. It also introduces an axiom (Axiom F) on crowding of functions, with consequences (Theorem 3) for the crowding of...

A fixed point theorem for branched covering maps of the plane

Alexander Blokh, Lex Oversteegen (2009)

Fundamenta Mathematicae

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It is known that every homeomorphism of the plane which admits an invariant non-separating continuum has a fixed point in the continuum. In this paper we show that any branched covering map of the plane of degree d, |d| ≤ 2, which has an invariant, non-separating continuum Y, either has a fixed point in Y, or is such that Y contains a minimal (in the sense of inclusion among invariant continua), fully invariant, non-separating subcontinuum X. In the latter case, f has to be of degree...

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.

Resolving a question of Arkhangel'skiĭ's

Michael G. Charalambous (2006)

Fundamenta Mathematicae

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We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.

Coverings and dimensions in infinite profinite groups

Peter Maga (2013)

Open Mathematics

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Answering a question of Miklós Abért, we prove that an infinite profinite group cannot be the union of less than continuum many translates of a compact subset of box dimension less than 1. Furthermore, we show that it is consistent with the axioms of set theory that in any infinite profinite group there exists a compact subset of Hausdorff dimension 0 such that one can cover the group by less than continuum many translates of it.