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Search: All articles in the CMB digital archive with keyword dense

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1. CMB 2012 (vol 56 pp. 477)

Ayadi, Adlene
Hypercyclic Abelian Groups of Affine Maps on $\mathbb{C}^{n}$
We give a characterization of hypercyclic abelian group $\mathcal{G}$ of affine maps on $\mathbb{C}^{n}$. If $\mathcal{G}$ is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by $n$ affine maps on $\mathbb{C}^{n}$ has a dense orbit.

Keywords:affine, hypercyclic, dense, orbit, affine group, abelian
Categories:37C85, 47A16

2. CMB 2012 (vol 56 pp. 860)

van Mill, Jan
On Countable Dense and $n$-homogeneity
We prove that a connected, countable dense homogeneous space is $n$-homogeneous for every $n$, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous space which is not strongly 2-homogeneous. This answers Problem 136 of Watson in the Open Problems in Topology Book in the negative.

Keywords:countable dense homogeneous, connected, $n$-homogeneous, strongly $n$-homogeneous, counterexample
Categories:54H15, 54C10, 54F05

3. CMB 2012 (vol 56 pp. 241)

Betsakos, Dimitrios; Pouliasis, Stamatis
Versions of Schwarz's Lemma for Condenser Capacity and Inner Radius
We prove variants of Schwarz's lemma involving monotonicity properties of condenser capacity and inner radius. Also, we examine when a similar monotonicity property holds for the hyperbolic metric.

Keywords:condenser capacity, inner radius, hyperbolic metric, Schwarz's lemma
Categories:30C80, 30F45, 31A15

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