Displaying similar documents to “Hyperspaces of infinite-dimensional compacta”

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.

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.

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.