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Abelian pro-countable groups and orbit equivalence relations

Maciej Malicki (2016)

Fundamenta Mathematicae

We study a class of abelian groups that can be defined as Polish pro-countable groups, as non-archimedean groups with a compatible two-sided invariant metric or as quasi-countable groups, i.e., closed subdirect products of countable discrete groups, endowed with the product topology. We show that for every non-locally compact, abelian quasi-countable group G there exists a closed L ≤ G and a closed, non-locally compact K ≤ G/L which is a direct product of discrete countable groups....

Absolute countable compactness of products and topological groups

Yan-Kui Song (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].

Adding machines, endpoints, and inverse limit spaces

Lori Alvin, Karen Brucks (2010)

Fundamenta Mathematicae

Let f be a unimodal map in the logistic or symmetric tent family whose restriction to the omega limit set of the turning point is topologically conjugate to an adding machine. A combinatoric characterization is provided for endpoints of the inverse limit space (I,f), where I denotes the core of the map.

Adequate Compacta which are Gul’ko or Talagrand

Čížek, Petr, Fabian, Marián (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 54H05, 03E15, 46B26We answer positively a question raised by S. Argyros: Given any coanalytic, nonalytic subset Σ′ of the irrationals, we construct, in Mercourakis space c1(Σ′), an adequate compact which is Gul’ko and not Talagrand. Further, given any Borel, non Fσ subset Σ′ of the irrationals, we construct, in c1(Σ′), an adequate compact which is Talagrand and not Eberlein.Supported by grants AV CR 101-90-03, and GA CR 201-01-1198

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