Fuzzy Sierpinski space (Q760686)

The author gives a definition of Sierpinski space in the fuzzy setting in a different manner. With \(S=I\) (the unit interval), \(u=\{\emptyset,S,i\}\), where \(i\in I^ I\) is the identity function, the author calls (S,u) the fuzzy Sierpinski space. For a category C with structure, the author shows that C is isomorphic to the category of fuzzy topological spaces iff there exists a fuzzy Sierpinski space (S,u) with underlying set [0,1] satisfying some specified conditions. The theorem is very near to its topological analogue.