# A model of quotient spaces

Topological Algebra and its Applications (2017)

- Volume: 5, Issue: 1, page 13-18
- ISSN: 2299-3231

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topHawete 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 -

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