On quasi-orbital space

• Autores: Hawete Hattab
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 1, 2017, págs. 53-59
• Idioma: inglés
• DOI: 10.4995/agt.2017.4676
• Enlaces
  • Texto completo
• Resumen

  • 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.  

• Referencias bibliográficas
  • 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.