On S-closed and Extremally Disconnected Fuzzy Topological Spaces
... sense and y 2 Cl u 6 1 ; , therefore every member of F is q-coincident with 1 ; , what is impossible. Hence y 2 . Almost regularity and 2 RO(X ) imply that 2 S (y ), i.e. there exists V 2 RO(X ) such that y q V 6 Cl V 6 . Since x 2= , then x q Cl V c = 1 ; Cl V is an open q-nbd of x ...
... sense and y 2 Cl u 6 1 ; , therefore every member of F is q-coincident with 1 ; , what is impossible. Hence y 2 . Almost regularity and 2 RO(X ) imply that 2 S (y ), i.e. there exists V 2 RO(X ) such that y q V 6 Cl V 6 . Since x 2= , then x q Cl V c = 1 ; Cl V is an open q-nbd of x ...
Characterizations of low separation axioms via α
... Example 3.1 Let (X, τ ) be a topological space such that X = {a, b, c, d} and τ = {∅, X, {a, b}}. Clearly, the set {a, c, d} is pD-set but it is not αD-set. Example 3.2 Let (X, τ ) be a topological space such that X = {a, b, c, d} and τ = {∅, X, {a}, {b}, {a, b}}. Clearly, the set {b, c, d} is sD-se ...
... Example 3.1 Let (X, τ ) be a topological space such that X = {a, b, c, d} and τ = {∅, X, {a, b}}. Clearly, the set {a, c, d} is pD-set but it is not αD-set. Example 3.2 Let (X, τ ) be a topological space such that X = {a, b, c, d} and τ = {∅, X, {a}, {b}, {a, b}}. Clearly, the set {b, c, d} is sD-se ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.