Quasihomeomorphisms and lattice equivalent topological spaces

Othman Echi; Sami Lazaar

doi:10.4995/agt.2009.1736

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

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