Abstract
The partially ordered sets have many times been an object of research of topologists. The interval topology on certain linearly ordered sets yields important examples of topological spaces. Many topologies for partially ordered sets have been defined—especially for lattices. This chapter discusses the concept of the compatibility of a topology and a partial order that are generalizations of the concept of Eilenberg. It presents the theorem that show the most important cases of topologies on partially ordered sets that are covered by the concept of compatibility.
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