Any \(T_1\) space has a continuous poset model (Q837638)

The authors study those topological spaces that have continuous models, that is, are homeomorphic to the space of maximal elements of a continuous partially ordered set. Their main result states that each \(T_1\) topological space has a continuous model. Their approach generalizes and modifies a machinery developed by Bennett and Lutzer. They also provide a bitopological characterization of those topological spaces that can be modeled by a continuous poset.