Quasi-orbit spaces associated to T₀-spaces

C. Bonatti, H. Hattab, and E. Salhi. "Quasi-orbit spaces associated to T₀-spaces." Fundamenta Mathematicae 211.3 (2011): 267-291. <http://eudml.org/doc/282708>.

@article{C2011,
abstract = {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.},
author = {C. Bonatti, H. Hattab, E. Salhi},
journal = {Fundamenta Mathematicae},
keywords = {quasi-orbit space; -space; Sierpiński space},
language = {eng},
number = {3},
pages = {267-291},
title = {Quasi-orbit spaces associated to T₀-spaces},
url = {http://eudml.org/doc/282708},
volume = {211},
year = {2011},
}

TY - JOUR
AU - C. Bonatti
AU - H. Hattab
AU - E. Salhi
TI - Quasi-orbit spaces associated to T₀-spaces
JO - Fundamenta Mathematicae
PY - 2011
VL - 211
IS - 3
SP - 267
EP - 291
AB - 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.
LA - eng
KW - quasi-orbit space; -space; Sierpiński space
UR - http://eudml.org/doc/282708
ER -