Order environments of topological spaces
An order environment of a~space~\(X\) is a~continuous poset~\(D\) such that \(X\) is homeomorphic to the space \(\text{Max}(D)\) of maximal points of~\(D\) with topology inherited from the Scott topology of~\(D\) and such that the Scott topology agree with Lawson topology at \(\text{Max}(D)\). During recent years some classes of spaces (locally compact Hausdorff spaces, complete metric spaces, and Polish spaces) were characterized by means of order environments or domain environments. In the paper under review, the author proves that a~space~\(X\) is Tychonoff if and only if it has a~continuous order environment.
scientific article; zbMATH DE number 2174207