Quasihomeomorphisms and lattice equivalent topological spaces

• Echi, Othman ^[1] ; Lazaar, Sami ^[2]
  1. [1] King Fahd University of Petroleum and Minerals

     King Fahd University of Petroleum and Minerals

     Arabia Saudí

     
  2. [2] University Tunis-El Manar
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 10, Nº. 2, 2009, págs. 227-237
• Idioma: inglés
• DOI: 10.4995/agt.2009.1736
• Enlaces
  • Texto completo
• Resumen

  • This paper deals with lattice-equivalence of topologica lspaces. We are concerned with two questions: the first one is when two topological spaces are lattice equivalent; the second one is what additional conditions have to be imposed on lattice equivalent spaces in order that they be homeomorphic. We give a contribution to the study of these questions. Many results of Thron [Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671-679] are recovered, clarified and commented.

• Referencias bibliográficas
  • K. Belaid, O. Echi and R. Gargouri, A-spectral spaces, Topology Appl. 138 (2004), 315–322. http://dx.doi.org/10.1016/j.topol.2003.08.009
  • E. Bouacida, O. Echi and E. Salhi, Foliations, spectral topology, and special morphisms, Advances in commutative ring theory (Fez, 1997),...
  • E. Bouacida, O. Echi and E. Salhi, Feuilletages et topologie spectrale, J. Math. Soc. Japan 52 (2000), 447–464. http://dx.doi.org/10.2969/jmsj/05220447
  • P. D. Finch, On the lattice-equivalence of topological spaces, J. Austral. Math. Soc. 6 (1966), 495–511. http://dx.doi.org/10.1017/S1446788700004973
  • A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique, Die Grundlehren der mathematischen Wissenschaften, 166, Springer-Verlag,...
  • A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique. I. Le langage des schemas, Inst. Hautes Etudes Sci. Publ. Math. No. 4,...
  • M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 43–60. http://dx.doi.org/10.1090/S0002-9947-1969-0251026-X
  • W. J. Thron, Lattice-equivalence of topological spaces, Duke Math. J. 29 (1962), 671–679. http://dx.doi.org/10.1215/S0012-7094-62-02968-X
  • K. W. Yip, Quasi-homeomorphisms and lattice-equivalences of topological spaces, J. Austral. Math. Soc. 14 (1972), 41–44. http://dx.doi.org/10.1017/S1446788700009617