EDB — 06V

Exercises

1. [06V] Prerequisites:[06M]↺↻,[06S]↺↻.(Solved on 2022-11-24) Let \((X,≤)\) be a directed set. Show that these properties are equivalent:

   • \((X,≤)\) satisfies the filtering property [(3.94)]↺↻,

   • \((X,≤)\) has no maximum,

   • \((X,≤)\) has no maximals.

   Solution 1

   [06W]↺↻