Complements in the lattice of uniformities
We present an example of a complete -bounded topological group which is not -factorizable. In addition, every -set in the group is open, but is not Lindelöf.
Let X be a Polish space, and let C₀ and C₁ be disjoint coanalytic subsets of X. The pair (C₀,C₁) is said to be complete if for every pair (D₀,D₁) of disjoint coanalytic subsets of there exists a continuous function such that and . We give several explicit examples of complete pairs of coanalytic sets.
In this paper, after giving the basic results related to the product of functions and the graph of functions in intuitionistic fuzzy topological spaces, we introduce and study the concept of fuzzy completely continuous functions between intuitionistic fuzzy topological spaces.
We conduct an investigation of the relationships which exist between various generalizations of complete regularity in the setting of merotopic spaces, with particular attention to filter spaces such as Cauchy spaces and convergence spaces. Our primary contribution consists in the presentation of several counterexamples establishing the divergence of various such generalizations of complete regularity. We give examples of: (1) a contigual zero space which is not weakly regular and is not a Cauchy...