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.
@article{bwmeta1.element.doi-10_1515_taa-2017-0003,
author = {Hawete Hattab},
title = {A model of quotient spaces},
journal = {Topological Algebra and its Applications},
volume = {5},
year = {2017},
pages = {13-18},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_taa-2017-0003}
}
Hawete Hattab. A model of quotient spaces. Topological Algebra and its Applications, Tome 5 (2017) pp. 13-18. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_taa-2017-0003/