On quasi-orbital space

Hawete Hattab

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 is the union of all orbits having the same closure as O. We denote by E=ethe space of classes of orbits called quasi-orbit space. A space is called a quasi-orbital space if it is homeomorphic to E=eG where 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.

 

 


Keywords

homeomorphism; group; quasi-orbit space; quasi-orbital space.

Subject classification

54F65; 54H20.

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References

C. Bonatti, H. Hattab and E. Salhi, Quasi-orbits spaces associated to $T_0$-spaces, Fund. Math. 211 (2011), 267-291.

http://dx.doi.org/10.4064/fm211-3-4

C. Bonatti, H. Hattab, E. Salhi and G. Vago, Hasse diagrams and orbit class spaces, Topology Appl. 158 (2011), 729-740.

http://dx.doi.org/10.1016/j.topol.2010.12.010

N. Bourbaki, Topologie générale chapitre 1 à 4, Masson, 1990.

J. Dugundji, Topology, Allyn and Bacon, Inc., Boston (1966).

R. Engelking, General Topology, 2nd ed., Helderman Verlag, Berlin, 1989.

W. H. Gottschalk and G. A. Hedlund, Topological Dynamics, AMS Colloquium Publications, Vol. 36, 1955.

H. Hattab, Characterization of quasi-orbit spaces, Qualitative theory of dynamical systems (2012).

H. Hattab and E. Salhi, Groups of homeomorphisms and spectral topology, Topology Proc. 28, no. 2 (2004), 503-526.

J. G. Hocking and G. S. Young, Topology, (1969).

J. L. Kelley, General Topology, Van Nostrand, New Work (1955).

N. Kopell, Commuting diffeomorphisms, Proc. Sympos. Pure Math. 14 (1970), 165-184.

http://dx.doi.org/10.1090/pspum/014/0270396

G. Reeb, Sur les structures feuilletées de codimension un et sur un théorème de A. Denjoy, Ann. Inst. Fourier 11 (1961), 185-200.

http://dx.doi.org/10.5802/aif.113

D. E. Miller, A selector for equivalence relations with $G_delta$ orbits, Proc. Amer. Math. Soc. 72, no. 2 (1978), 365-369.

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