“Research Note” TOPOLOGICAL RING
... A topological groupoid is a groupoid R such that the sets R and R0 are topological spaces, and source, target, object, inverse and composition maps are continuous. Let R and H be two topological groupoids. A morphism of topological groupoids is a pair of maps f:H→R and f0:H0→R0 such that f and f0 ar ...
... A topological groupoid is a groupoid R such that the sets R and R0 are topological spaces, and source, target, object, inverse and composition maps are continuous. Let R and H be two topological groupoids. A morphism of topological groupoids is a pair of maps f:H→R and f0:H0→R0 such that f and f0 ar ...
On some locally closed sets and spaces in Ideal Topological
... (ii) A = Ucl(A) for some δ̂ s - open set U. (iii) cl(A) – A is δ̂ s - closed. (iv) A(X–cl(A)) is δ̂ s - open. Proof. (i)(ii) If A δ̂ sILC, then there exist a δ̂ s – open set U and a -I-closed set F such that A = UF. Clearly AUcl(A). Since F is -I-closed, cl(A) cl(F) = F and so Uc ...
... (ii) A = Ucl(A) for some δ̂ s - open set U. (iii) cl(A) – A is δ̂ s - closed. (iv) A(X–cl(A)) is δ̂ s - open. Proof. (i)(ii) If A δ̂ sILC, then there exist a δ̂ s – open set U and a -I-closed set F such that A = UF. Clearly AUcl(A). Since F is -I-closed, cl(A) cl(F) = F and so Uc ...
Full Text
... For any point x of a topological space (X, τ ), τ (x) denotes the collection of all open neighborhoods of x. 2.1. Definition. [14] Let (X, τ ) be a topological space and G be a grill on X. A mapping Φ : P(X) → P(X) is defined as follows: Φ(A) = ΦG (A, τ ) = {x ∈ X : A ∩ U ∈ G for all U ∈ τ (x)} for ...
... For any point x of a topological space (X, τ ), τ (x) denotes the collection of all open neighborhoods of x. 2.1. Definition. [14] Let (X, τ ) be a topological space and G be a grill on X. A mapping Φ : P(X) → P(X) is defined as follows: Φ(A) = ΦG (A, τ ) = {x ∈ X : A ∩ U ∈ G for all U ∈ τ (x)} for ...
Print this article - Innovative Journal
... A function f : (X, τ) → (Y, σ) is said to be semicontinuous[9] (resp. α-continuous [12], pre-continuous [11], totally continuous [7], totally semi-continuous [16]) if the inverse image of every open subset of (Y, σ) is a semi-open (resp. α-open, preopen, clopen, semi-clopen) subset of (X,τ). Definit ...
... A function f : (X, τ) → (Y, σ) is said to be semicontinuous[9] (resp. α-continuous [12], pre-continuous [11], totally continuous [7], totally semi-continuous [16]) if the inverse image of every open subset of (Y, σ) is a semi-open (resp. α-open, preopen, clopen, semi-clopen) subset of (X,τ). Definit ...
- Journal of Linear and Topological Algebra
... open sets [16] and semi-preopen sets [13] . Multifunctions and of course continuous multifunctions stand among the most important and most researched points in the whole of the mathematical science. Many different forms of continuous multifunctions have been introduced over the years. Csaszar [1] in ...
... open sets [16] and semi-preopen sets [13] . Multifunctions and of course continuous multifunctions stand among the most important and most researched points in the whole of the mathematical science. Many different forms of continuous multifunctions have been introduced over the years. Csaszar [1] in ...
Topology 550A Homework 3, Week 3 (Corrections
... Proof . Consider, for α ∈ A, U = α Gα s.t. Gα are the basic neighborhoods, that is, the usual open disks centered at x that lie above the x-axis. It follows that U in in Γ. When we take the closure of U, ...
... Proof . Consider, for α ∈ A, U = α Gα s.t. Gα are the basic neighborhoods, that is, the usual open disks centered at x that lie above the x-axis. It follows that U in in Γ. When we take the closure of U, ...
On Maps and Generalized Λb-Sets
... The converse needs not be true as seen from the following example. Example 3.5. Let X = Y = {a, b, c}, τ = {∅, {a}, X} and σ = {∅, {a, b}, Y }. The identity map f : (X, τ ) → (Y, σ) is g.Λb-continuous but is not g.Λb -irresolute since for the g.Λb -set {b} of (Y, σ), the inverse image f −1 ({b}) = { ...
... The converse needs not be true as seen from the following example. Example 3.5. Let X = Y = {a, b, c}, τ = {∅, {a}, X} and σ = {∅, {a, b}, Y }. The identity map f : (X, τ ) → (Y, σ) is g.Λb-continuous but is not g.Λb -irresolute since for the g.Λb -set {b} of (Y, σ), the inverse image f −1 ({b}) = { ...
PDF file without embedded fonts
... begin with two disjoint subsets C; D R and for each x 2 D a sequence hxn i in C converging to x. They let X(C; D) be the union C [ D but with points of C isolated and neighbourhoods of points of D containing tails of the corresponding sequences. The essential features of X(C; D) are then preserved ...
... begin with two disjoint subsets C; D R and for each x 2 D a sequence hxn i in C converging to x. They let X(C; D) be the union C [ D but with points of C isolated and neighbourhoods of points of D containing tails of the corresponding sequences. The essential features of X(C; D) are then preserved ...
