EDB — 0HS

[0HS] Topics:directed ordering.Prerequisites:[06N]↺↻.

Let \((J,≤)\) be a set with direct ordering. We decide that an ”open set” in \(J\) is a set \(A\) that contains a ”half-line” of the form \(\{ k∈ J : k≥ j\} \) (for a \(j∈ J\))  ¹ . Let therefore \(𝜏\) be the family of all such open sets, to which we add \(∅,J\). Show that \(𝜏\) is a topology. Is this topology Hausdorff? What are the accumulation points?