Definition:Sober Space/Separation vs Completeness
Jump to navigation
Jump to search
Definition: Separation Axiom vs Completeness Property
In some sources sobriety is listed among the separation axioms.
It has been pointed out in other sources that sobriety is a property of completeness type, similar to the completeness of metric spaces.
From Sober Space iff Completely Prime Filter is Unique System of Open Neighborhoods, filters of open sets that look like systems of open neighborhoods are required to really be systems of open neighborhoods.