Displaying similar documents to “Topological entropy on zero-dimensional spaces”

Endomorphism algebras over large domains

Rüdiger Göbel, Simone Pabst (1998)

Fundamenta Mathematicae

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The paper deals with realizations of R-algebras A as endomorphism algebras End G ≅ A of suitable R-modules G over a commutative ring R. We are mainly interested in the case of R having "many prime ideals", such as R = ℝ[x], the ring of real polynomials, or R a non-discrete valuation domain

On entropy of patterns given by interval maps

Jozef Bobok (1999)

Fundamenta Mathematicae

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Defining the complexity of a green pattern exhibited by an interval map, we give the best bounds of the topological entropy of a pattern with a given complexity. Moreover, we show that the topological entropy attains its strict minimum on the set of patterns with fixed eccentricity m/n at a unimodal X-minimal case. Using a different method, the last result was independently proved in[11].

Modules commuting (via Hom) with some limits

Robert El Bashir, Tomáš Kepka (1998)

Fundamenta Mathematicae

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For every module M we have a natural monomorphism   Φ : ∐ i ∈ I H o m R ( A i , M ) → H o m R ( ∏ i ∈ I A i , M ) and we focus attention on the case when Φ is also an epimorphism. The corresponding modules M depend on thickness of the cardinal number card(I). Some other limits are also considered.

Subcontinua of inverse limit spaces of unimodal maps

Karen Brucks, Henk Bruin (1999)

Fundamenta Mathematicae

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We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal...