On ultraconnected spaces (Q912427)

Summary: A topological space is ultraconnected if the intersection of any two nonempty closed sets is nonempty. The author studies some properties of ultraconnected spaces and shows that ultraconnected \(T_{{1/2}}\) spaces are maximal ultraconnected and minimal \(T_{{1/2}}\). He also introduces the notion of F-connected spaces, topological spaces which are both hyperconnected and ultraconnected and characterizes compact maximal F- connected topologies on a set.