On quasi-orbital space

Hawete Hattab

Abstract

Let be a subgroup of the group Homeo(E) of homeomorphisms of a Hausdorff topological space E. The class of an orbit 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=ewhere 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.

 

 

 

 


Keywords

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

Subject classification

54F65; 54H20

Full Text:

PDF

References

C. Bonatti, H. Hattab and E. Salhi, Quasi-orbits spaces associated to $T_0$-spaces, Fund. Math. 211 (2011), 267-291. https://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. https://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. https://doi.org/10.1090/coll/036

H. Hattab, Characterization of quasi-orbit spaces, Qualitative theory of dynamical systems (2012). https://doi.org/10.1007/s12346-011-0066-5

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. https://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. https://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. https://doi.org/10.2307/2042808

Abstract Views

1147
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt