On CDH fuzzy spaces

Densely homogeneous fuzzy spaces

“…The following definitions and propositions will be used in the sequel: Definition 2.1. [9] Let be a non-empty set, be a non-empty subset of and be a collection of fuzzy points in . Then  ℚ( ) will denote the set ℚ( ) = { : is a fuzzy point with ∈ and r ∈ ℚ ∩ (0,1)}.…”

“…Mathematicians extended many topological concepts to include fuzzy topological spaces such as: separation axioms, connectedness, compactness and metrizability. Several fuzzy homogeneity concepts were discussed in [3][4][5][6][7][8][9][10][11]. A separable topological space (X, τ) is countable dense homogeneous (CDH) [12] if given any two countable dense subsets A and B of (X, τ) there is a homeomorphism f: (X, τ) → (X, τ) such that f(A) = B.…”

“…The study of CDH topological spaces and their related concepts is still a hot area of research, as appears in [13][14][15][16][17][18][19][20] and other papers. Recently, authors in [9] extended CDH topological property to include fuzzy topological spaces. They proved that their extension is a good extension in the sense of Lowen, and proved that a-cut topological space (X, ℑ a ) of a CDH fuzzy topological space (X, ℑ) is CDH in general only for a = 0.…”

Fuzzy n-s-homogeneity and fuzzy weak n-s-homogeneity

“…, . Several fuzzy homogeneity concepts were discussed in [5][6][7][8][9][10][11][12][13][14]. Let ( , ℑ₁, ℑ₂) and ( , ₁, ₂) be two fuzzy bitopological spaces.…”

“…( , | ₁, | ₂) is fuzzy n-homogeneous. Proposition 1.3 [11]. Let ( , ℑ) be a fuzzy topological space and let : ( , ℑ) → ( , ℑ) be a fuzzy continuous (homeomorphism) map.…”