Quasihomeomorphisms and lattice equivalent topological spaces

Authors

  • Othman Echi King Fahd University of Petroleum and Minerals
  • Sami Lazaar University Tunis-El Manar

DOI:

https://doi.org/10.4995/agt.2009.1736

Keywords:

Quasihomeomorphism, Lattice equivalence, Sober space, TD- space

Abstract

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.

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Author Biographies

Othman Echi, King Fahd University of Petroleum and Minerals

King Fahd University of Petroleum and Minerals, Department of Mathematics & Statistics, P.O. Box 5046, Dhahran 31261, Saudi Arabia.

Sami Lazaar, University Tunis-El Manar

Department of Mathematics, University Tunis-El Manar, Faculty of Sciences of Tunis "Campus Universitaire", 2092 Tunis, Tunisia

References

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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, New York, 1971.

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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

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How to Cite

[1]
O. Echi and S. Lazaar, “Quasihomeomorphisms and lattice equivalent topological spaces”, Appl. Gen. Topol., vol. 10, no. 2, pp. 227–237, Oct. 2009.

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Articles