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A class of continua that are not attractors of any IFS

100%

Kulczycki M., Nowak M.

Open Mathematics

2012

tom 10

nr 6

2073-2076

This paper presents a sufficient condition for a continuum in ℝn to be embeddable in ℝn in such a way that its image is not an attractor of any iterated function system. An example of a continuum in ℝ2 that is not an attractor of any weak iterated function system is also given.

Coverings and dimensions in infinite profinite groups

75%

Maga P.

Open Mathematics

2013

tom 11

nr 2

246-253

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.

Ograniczanie wyników

2 Open Mathematics

1 Kulczycki M.

1 Maga P.

1 Nowak M.

1 2013

1 2012

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A class of continua that are not attractors of any IFS

Coverings and dimensions in infinite profinite groups