Quasihomeomorphisms and lattice equivalent topological spaces

Othman Echi

Saudi Arabia

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

Tunisia

University Tunis-El Manar

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

Submitted: 2013-09-30

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Accepted: 2013-09-30

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

Quasihomeomorphism, Lattice equivalence, Sober space, TD- space

Supporting agencies:

This research was not funded

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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