On quasi-orbital space

Hawete Hattab

Saudi Arabia

Umm Al-Qura University

Math department

Submitted: 2016-02-09

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Accepted: 2016-07-12

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Published: 2017-04-03

DOI: https://doi.org/10.4995/agt.2017.4676
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Keywords:

homeomorphism, group, quasi-orbit space, quasi-orbital space

Supporting agencies:

Laboratoire des systmes dynamique et combinatoire

Facult des Sciences de Sfax

Tunisia.

Abstract:

Let G be a subgroup of the group Homeo(E) of homeomorphisms of a Hausdorff topological space E. The class of an orbit O of G  is the union of all orbits having the same closure as O. We denote by E=eG  the space of classes of orbits called quasi-orbit space. A space X  is called a quasi-orbital space if it is homeomorphic to E=eG where E  is a compact Hausdorff space. In this paper, we show that every in nite second countable quasi-compact T0-space is the quotient of a quasi-orbital space.

 

 

 

 

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