A model of quotient spaces

• Autorzy: Hawete Hattab
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Homotopy; orbit space; leaf space; leaf class space; orbit class space

Kategorie tematyczne

• 18B35: Preorders, orders and lattices (viewed as categories)
• 55P15: Classification of homotopy type
• 54F65: Topological characterizations of particular spaces
• 55P10: Homotopy equivalences
• 54B15: Quotient spaces, decompositions

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2017
• Tom: 5
• Numer: 1
• Strony: 13-18

Daty

wydano

2017-04-25

otrzymano

2015-11-03

zaakceptowano

2016-11-01

online

2017-06-01

Twórcy

autor

Hawete Hattab

• ,

Identyfikatory

DOI

10.1515/taa-2017-0003