Displaying similar documents to “Coverings and dimensions in infinite profinite groups”

Covering the real line with translates of a zero-dimensional compact set

András Máthé (2011)

Fundamenta Mathematicae

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We construct a compact set C of Hausdorff dimension zero such that cof(𝒩) many translates of C cover the real line. Hence it is consistent with ZFC that less than continuum many translates of a zero-dimensional compact set can cover the real line. This answers a question of Dan Mauldin.

Smoothness and the property of Kelley

Janusz Jerzy Charatonik, Włodzimierz J. Charatonik (2000)

Commentationes Mathematicae Universitatis Carolinae

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Interrelations between smoothness of a continuum at a point, pointwise smoothness, the property of Kelley at a point and local connectedness are studied in the paper.

AANR spaces and absolute retracts for tree-like continua

Janusz Jerzy Charatonik, Janusz R. Prajs (2005)

Czechoslovak Mathematical Journal

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Continua that are approximative absolute neighborhood retracts (AANR’s) are characterized as absolute terminal retracts, i.e., retracts of continua in which they are embedded as terminal subcontinua. This implies that any AANR continuum has a dense arc component, and that any ANR continuum is an absolute terminal retract. It is proved that each absolute retract for any of the classes of: tree-like continua, λ -dendroids, dendroids, arc-like continua and arc-like λ -dendroids is an approximative...

Hyperspaces of Peano continua of euclidean spaces

Helma Gladdines, Jan van Mill (1993)

Fundamenta Mathematicae

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If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space L ( ℝ n ) is homeomorphic to B ∞ , where B denotes the pseudo-boundary of the Hilbert cube Q.