Homeomorphism groups of Sierpiński carpets and Erdős space

• Autorzy: Jan J. Dijkstra , Dave Visser
• Języki publikacji: EN

Abstrakty

EN

Erdős space 𝔈 is the "rational" Hilbert space, that is, the set of vectors in ℓ² with all coordinates rational. Erdős proved that 𝔈 is one-dimensional and homeomorphic to its own square 𝔈 × 𝔈, which makes it an important example in dimension theory. Dijkstra and van Mill found topological characterizations of 𝔈. Let $Mₙ^{n+1}$, n ∈ ℕ, be the n-dimensional Menger continuum in $ℝ^{n+1}$, also known as the n-dimensional Sierpiński carpet, and let D be a countable dense subset of $Mₙ^{n+1}$. We consider the topological group $𝓗(Mₙ^{n+1},D)$ of all autohomeomorphisms of $Mₙ^{n+1}$ that map D onto itself, equipped with the compact-open topology. We show that under some conditions on D the space $𝓗(Mₙ^{n+1},D)$ is homeomorphic to 𝔈 for n ∈ ℕ ∖ {3}.

Kategorie tematyczne

• 57S05: Topological properties of groups of homeomorphisms or diffeomorphisms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 207
• Numer: 1
• Strony: 1-19

Daty

wydano

2010

Twórcy

autor

Jan J. Dijkstra

• Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

autor

Dave Visser

• Faculteit der Exacte Wetenschappen/Afdeling Wiskunde, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

Identyfikatory

DOI

10.4064/fm207-1-1