some good extensions of compactness inšostak`s l-fuzzy
... (1) f is called fuzzy semi-open iff for every p ∈ Pr (L) there exists g ∈ LX with T(g) 6≤ p such that g ≤ f ≤ cl (g). (2) f is called fuzzy α-open iff for every p ∈ Pr (L) there exists g ∈ LX with T(g) 6≤ p such that g ≤ f ≤ int (cl (g)). (3) f is called fuzzy regular open iff f = int (cl (f )). (4) ...
... (1) f is called fuzzy semi-open iff for every p ∈ Pr (L) there exists g ∈ LX with T(g) 6≤ p such that g ≤ f ≤ cl (g). (2) f is called fuzzy α-open iff for every p ∈ Pr (L) there exists g ∈ LX with T(g) 6≤ p such that g ≤ f ≤ int (cl (g)). (3) f is called fuzzy regular open iff f = int (cl (f )). (4) ...
ON A CLASS OF SETS VIA GRILL : A DECOMPOSITION OF
... decompositions of continuous function. A classical example towards decomposition of continuity is the paper of N. Levine [6], whereas a very recent attempt by Hatir and Jafari [5] with the same motivation has culminated in the introduction and study of Φ-open sets, where Φ is a suitable operator. Th ...
... decompositions of continuous function. A classical example towards decomposition of continuity is the paper of N. Levine [6], whereas a very recent attempt by Hatir and Jafari [5] with the same motivation has culminated in the introduction and study of Φ-open sets, where Φ is a suitable operator. Th ...
An Introduction to Simplicial Sets
... In this section, we define simplicial sets without providing motivation, and we describe the combinatorial data necessary for specifying a simplicial set. We then try to build intuition by bringing in the geometric notion of simplices from algebraic topology. We first define the category ∆, a visual ...
... In this section, we define simplicial sets without providing motivation, and we describe the combinatorial data necessary for specifying a simplicial set. We then try to build intuition by bringing in the geometric notion of simplices from algebraic topology. We first define the category ∆, a visual ...
Closure Operators in Semiuniform Convergence Spaces
... Note that every semiuniform convergence spaces (B, =) has an underlying Kent convergence spaces (B, qγ= ) defined as follows: qγ= = {(α, x) : α ∩ [x] ∈ γ= }, where γ= = {β ∈ F(B) : β × β ∈ =} [32] or [30]. 3. Closed Subsets of Semiuniform Spaces In this section, we characterize the (strongly) closed ...
... Note that every semiuniform convergence spaces (B, =) has an underlying Kent convergence spaces (B, qγ= ) defined as follows: qγ= = {(α, x) : α ∩ [x] ∈ γ= }, where γ= = {β ∈ F(B) : β × β ∈ =} [32] or [30]. 3. Closed Subsets of Semiuniform Spaces In this section, we characterize the (strongly) closed ...
Topology
... Topology is an important, classical part of mathematics. It deals with interesting objects (the Klein bottle, Bing’s house, manifolds, lens spaces, knots, . . . ). To study it in detail is a considerable enterprise (a huge subject with many subtle sub-disciplines and methods); here, however, we are ...
... Topology is an important, classical part of mathematics. It deals with interesting objects (the Klein bottle, Bing’s house, manifolds, lens spaces, knots, . . . ). To study it in detail is a considerable enterprise (a huge subject with many subtle sub-disciplines and methods); here, however, we are ...
A unified theory of weakly contra-(µ, λ)
... Definition 4.1. Let (X, τ ) be a topological space. A subset A of X is said to be 1. g-closed [41] if Cl(A) ⊂ U whenever A ⊂ U and U ∈ τ , 2. αg-closed [27] if αCl(A) ⊂ U whenever A ⊂ U and U ∈ τ , 3. gs-closed [26] if sCl(A) ⊂ U whenever A ⊂ U and U ∈ τ , 4. gp-closed [6] if pCl(A) ⊂ U whenever A ⊂ ...
... Definition 4.1. Let (X, τ ) be a topological space. A subset A of X is said to be 1. g-closed [41] if Cl(A) ⊂ U whenever A ⊂ U and U ∈ τ , 2. αg-closed [27] if αCl(A) ⊂ U whenever A ⊂ U and U ∈ τ , 3. gs-closed [26] if sCl(A) ⊂ U whenever A ⊂ U and U ∈ τ , 4. gp-closed [6] if pCl(A) ⊂ U whenever A ⊂ ...
Free full version - topo.auburn.edu
... be a uniformly continuous map wllere (Y, v) is a locally finite nearness space. Defi11e h: (X,T(fJ~)) ~ (Y,v) by h(x) == g(x) for all x EX. To see that h is uniformly contillUOUS let C E v. Then there exists P E v such that P is locall:y finite and refines C. Now int(P) is in v and is also locally f ...
... be a uniformly continuous map wllere (Y, v) is a locally finite nearness space. Defi11e h: (X,T(fJ~)) ~ (Y,v) by h(x) == g(x) for all x EX. To see that h is uniformly contillUOUS let C E v. Then there exists P E v such that P is locall:y finite and refines C. Now int(P) is in v and is also locally f ...
