Dcpos and convergence spaces I: Scott and Heckmann convergences

Every dcpo can be seen as a topological space, once we equip it with the Scott topology. And every topological space can be seen as a convergence space, so every dcpo can be seen as a convergence space.  In 2003, Reinhold Heckmann observed that we could see dcpos as convergence spaces in another way, with some serendipitous properties.  We shall see what serendipitous properties next time.  This month, we shall prepare the grounds for that piece of work, by investigating various convergences that can be put on dcpos, in particular one introduced by Dana S. Scott way earlier.  Read the full post.