A model of quotient spaces

Hawete Hattab. "A model of quotient spaces." Topological Algebra and its Applications 5.1 (2017): 13-18. <http://eudml.org/doc/288583>.

@article{HaweteHattab2017,
abstract = {Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃ ̃ℜ̅ is called the trajectory class space. In this paper, we show that the space E/̃ ̃ℜ̅ is a simple model of the quotient space E/R. This model can provide a finite model. Some applications to orbit spaces of groups of homeomorphisms and leaf spaces are given.},
author = {Hawete Hattab},
journal = {Topological Algebra and its Applications},
keywords = {Homotopy; orbit space; leaf space; leaf class space; orbit class space},
language = {eng},
number = {1},
pages = {13-18},
title = {A model of quotient spaces},
url = {http://eudml.org/doc/288583},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Hawete Hattab
TI - A model of quotient spaces
JO - Topological Algebra and its Applications
PY - 2017
VL - 5
IS - 1
SP - 13
EP - 18
AB - Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃ ̃ℜ̅ is called the trajectory class space. In this paper, we show that the space E/̃ ̃ℜ̅ is a simple model of the quotient space E/R. This model can provide a finite model. Some applications to orbit spaces of groups of homeomorphisms and leaf spaces are given.
LA - eng
KW - Homotopy; orbit space; leaf space; leaf class space; orbit class space
UR - http://eudml.org/doc/288583
ER -