Chapter 5 Countability and Separation Axioms
... U = RK{xnk : k ∈ N} is an open set in X containing x. Hence {xn } converges to x in X implies there exists n0 ∈ N such that xn ∈ U for all n ≥ n0 . In particular for k ≥ n0 , nk ≥ k ≥ n0 and this implies xnk ∈ U .) So we have the following: xn → x in X implies f (xn ) → f (x) in Y. But the given fun ...
... U = RK{xnk : k ∈ N} is an open set in X containing x. Hence {xn } converges to x in X implies there exists n0 ∈ N such that xn ∈ U for all n ≥ n0 . In particular for k ≥ n0 , nk ≥ k ≥ n0 and this implies xnk ∈ U .) So we have the following: xn → x in X implies f (xn ) → f (x) in Y. But the given fun ...
On upper and lower ω-irresolute multifunctions
... interior of A with respect to τ, respectively. Recently, as generalization of closed sets, the notion of ω-closed sets were introduced and studied by Hdeib [9]. A point x ∈ X is called a condensation point of A if for each U ∈ τ with x ∈ U, the set U ∩ A is uncountable. A is said to be ω-closed [9] ...
... interior of A with respect to τ, respectively. Recently, as generalization of closed sets, the notion of ω-closed sets were introduced and studied by Hdeib [9]. A point x ∈ X is called a condensation point of A if for each U ∈ τ with x ∈ U, the set U ∩ A is uncountable. A is said to be ω-closed [9] ...
SOFT TOPOLOGICAL QUESTIONS AND ANSWERS M. Matejdes
... on F(A, X) stated in Definition 2.1 or by the corresponding relation operations. For example ⊔t∈T (Gt , A) = (∪t∈T Gt , A) = (F∪t∈T RGt , A). From the one-to-one correspondence between the relations from R(A, X) and the set valued mappings from F(A, X), a soft topological space can be characterizes ...
... on F(A, X) stated in Definition 2.1 or by the corresponding relation operations. For example ⊔t∈T (Gt , A) = (∪t∈T Gt , A) = (F∪t∈T RGt , A). From the one-to-one correspondence between the relations from R(A, X) and the set valued mappings from F(A, X), a soft topological space can be characterizes ...
ON FAINTLY SEMIGENERALIZED α
... Definition 29. A graph G(f ) of a function f : (X, τ ) → (Y, σ) is said to be θ-sgα-closed if for each (x, y) ∈ (X × Y )\G(f ), there exist U ∈ sgαO(X, x) and V ∈ σθ containing y such that (U × V ) ∩ G(f ) = ∅. Lemma 30. A graph G(f ) of a function f : (X, τ ) → (Y, σ) is θ-sgαclosed in X × Y if and ...
... Definition 29. A graph G(f ) of a function f : (X, τ ) → (Y, σ) is said to be θ-sgα-closed if for each (x, y) ∈ (X × Y )\G(f ), there exist U ∈ sgαO(X, x) and V ∈ σθ containing y such that (U × V ) ∩ G(f ) = ∅. Lemma 30. A graph G(f ) of a function f : (X, τ ) → (Y, σ) is θ-sgαclosed in X × Y if and ...
Abstracts of Papers
... rings are Jaffard. Furthermore, we introduce a new invariant allowing us to compute the number of Jaffard domains between any given extension of integral domains A ⊆ B. We also give a new characterization of valuation domains and one-dimensional Prfer domains and provide many examples to illustrate ...
... rings are Jaffard. Furthermore, we introduce a new invariant allowing us to compute the number of Jaffard domains between any given extension of integral domains A ⊆ B. We also give a new characterization of valuation domains and one-dimensional Prfer domains and provide many examples to illustrate ...
