Displaying similar documents to “Imposing psendocompact group topologies on Abeliau groups”

Representation of finite abelian group elements by subsequence sums

David J. Grynkiewicz, Luz E. Marchan, Oscar Ordaz (2009)

Journal de Théorie des Nombres de Bordeaux

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Let G ≅ C n 1 ⊕ ... ⊕ C n r be a finite and nontrivial abelian group with n 1 | n 2 | ... | n r . A conjecture of Hamidoune says that if W = w 1 · ... · w n is a sequence of integers, all but at most one relatively prime to | G | , and S is a sequence over G with | S | ≥ | W | + | G | - 1 ≥ | G | + 1 , the maximum multiplicity of S at most | W | , and σ ( W ) ≡ 0 mod | G | , then there exists a nontrivial subgroup H such that every element g ∈ H can be represented as a weighted subsequence sum of the form g = ∑ n i = 1 w i s i , with s 1 · ... · s n a subsequence of S . We give two examples showing this does not hold in general, and characterize the...

Linear subspace of Rl without dense totally disconnected subsets

K. Ciesielski (1993)

Fundamenta Mathematicae

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In [1] the author showed that if there is a cardinal κ such that 2 κ = κ + then there exists a completely regular space without dense 0-dimensional subspaces. This was a solution of a problem of Arkhangel’skiĭ. Recently Arkhangel’skiĭ asked the author whether one can generalize this result by constructing a completely regular space without dense totally disconnected subspaces, and whether such a space can have a structure of a linear space. The purpose of this paper is to show that indeed such...

Characterizations of groups generated by Kronecker sets

András Biró (2007)

Journal de Théorie des Nombres de Bordeaux

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In recent years, starting with the paper [B-D-S], we have investigated the possibility of characterizing countable subgroups of the torus T = R / Z by subsets of Z . Here we consider new types of subgroups: let K ⊆ T be a Kronecker set (a compact set on which every continuous function f : K → T can be uniformly approximated by characters of T ), and G the group generated by K . We prove (Theorem 1) that G can be characterized by a subset of Z 2 (instead of a subset of Z ). If K is finite, Theorem 1 implies our...

Forcing countable networks for spaces satisfying R ( X ω ) = ω

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (1996)

Commentationes Mathematicae Universitatis Carolinae

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We show that all finite powers of a Hausdorff space X do not contain uncountable weakly separated subspaces iff there is a c.c.c poset P such that in V P X is a countable union of 0 -dimensional subspaces of countable weight. We also show that this theorem is sharp in two different senses: (i) we cannot get rid of using generic extensions, (ii) we have to consider all finite powers of X .

The Bohr compactification, modulo a metrizable subgroup

W. Comfort, F. Trigos-Arrieta, S. Wu (1993)

Fundamenta Mathematicae

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The authors prove the following result, which generalizes a well-known theorem of I. Glicksberg [G]: If G is a locally compact Abelian group with Bohr compactification bG, and if N is a closed metrizable subgroup of bG, then every A ⊆ G satisfies: A·(N ∩ G) is compact in G if and only if {aN:a ∈ A} is compact in bG/N. Examples are given to show: (a) the asserted equivalence can fail in the absence of the metrizability hypothesis, even when N ∩ G = {1}; (b) the asserted equivalence can...