Quasi-orbit spaces associated to T₀-spaces

• Autorzy: C. Bonatti , H. Hattab , E. Salhi
• Języki publikacji: EN

Abstrakty

EN

Let G ⊂ Homeo(E) be a group of homeomorphisms of a topological space E. The class of an orbit O of G is the union of all orbits having the same closure as O. Let E/G̃ be the space of classes of orbits, called the quasi-orbit space. We show that every second countable T₀-space Y is a quasi-orbit space E/G̃, where E is a second countable metric space. The regular part X₀ of a T₀-space X is the union of open subsets homeomorphic to ℝ or to 𝕊¹. We give a characterization of the spaces X with finite singular part X-X₀ which are the quasi-orbit spaces of countable groups G ⊂ Homeo₊(ℝ). Finally we show that every finite T₀-space is the singular part of the quasi-leaf space of a codimension one foliation on a closed three-manifold.

Kategorie tematyczne

• 54H20: Topological dynamics
• 54F65: Topological characterizations of particular spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 211
• Numer: 3
• Strony: 267-291

Daty

wydano

2011

Twórcy

autor

C. Bonatti

• IMB, UMR 5584 du CNRS, 9 av. Alain Savary, 21000 Dijon, France

autor

H. Hattab

• Institut Supérieur, d'Informatique et du Multimedia, Route de Tunis km 10, B.P. 242, Sfax 3021, Tunisia

autor

E. Salhi

• Département de Mathématiques, Faculté des Sciences de Sfax, Route de Soukra km 3.5, B.P. 802, Sfax 3018, Tunisia

Identyfikatory

DOI

10.4064/fm211-3-4