Quasihomeomorphisms and lattice equivalent topological spaces

Othman Echi, Sami Lazaar
DOI: https://doi.org/10.4995/agt.2009.1736

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.

Keywords

Quasihomeomorphism; Lattice equivalence; Sober space; TD- space

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References

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), 111–132, Lecture Notes in Pure and Appl. Math. 205, Dekker, New York, 1999.

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, New York, 1971.

A. Grothendieck and J. Dieudonné, Eléments de Géométrie Algébrique. I. Le langage des schemas, Inst. Hautes Etudes Sci. Publ. Math. No. 4, 1960.

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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