![arXiv:0706.3441v1 [math.AG] 25 Jun 2007](http://s1.studyres.com/store/data/017784481_1-dd1160ad974ad834977ad61a663d12c3-300x300.png)
properties of fuzzy metric space and its applications
... 5.3.1 Theorem- The element A of a fuzzy metric space (F x .µ x ) is an Fadherent point of the subset G of F x iff d (A,G)=0 Proof: we have d(A,G)= inf. {µ x (A.y): y∈G} Therefore d(A,G)=0 ⇒ every F-open sphere S (A,r) contains element of G. which implies A is an F-adherent point of G. conversely if ...
... 5.3.1 Theorem- The element A of a fuzzy metric space (F x .µ x ) is an Fadherent point of the subset G of F x iff d (A,G)=0 Proof: we have d(A,G)= inf. {µ x (A.y): y∈G} Therefore d(A,G)=0 ⇒ every F-open sphere S (A,r) contains element of G. which implies A is an F-adherent point of G. conversely if ...
Lecture Notes (unique pdf file)
... ⇒ Let (X, τ ) be a topological space, x ∈ X and F(x) the filter of neighbourhoods of x. Then (N1) trivially holds by definition of neighbourhood of x. To show (N2), let us take A ∈ F(x). Since A is a neighbourhood of x, there exists B ∈ τ s.t. x ∈ B ⊆ A. Then clearly B ∈ F(x). Moreover, since for an ...
... ⇒ Let (X, τ ) be a topological space, x ∈ X and F(x) the filter of neighbourhoods of x. Then (N1) trivially holds by definition of neighbourhood of x. To show (N2), let us take A ∈ F(x). Since A is a neighbourhood of x, there exists B ∈ τ s.t. x ∈ B ⊆ A. Then clearly B ∈ F(x). Moreover, since for an ...
ON WEAKLY e-CONTINUOUS FUNCTIONS
... A subset A of a space X is called regular open [23] (resp. regular closed [23]) if A = int(cl(A)) (resp. A = cl(int(A))). A subset A of a space X is called δ-semiopen [19] (resp. preopen [12], δ-preopen [22], α-open [14], semi-preopen [3] or β-open [1], b-open [2] or sp-open [5] or γ-open [8], e-ope ...
... A subset A of a space X is called regular open [23] (resp. regular closed [23]) if A = int(cl(A)) (resp. A = cl(int(A))). A subset A of a space X is called δ-semiopen [19] (resp. preopen [12], δ-preopen [22], α-open [14], semi-preopen [3] or β-open [1], b-open [2] or sp-open [5] or γ-open [8], e-ope ...
65, 3 (2013), 419–424 September 2013 TOTALLY BOUNDED ENDOMORPHISMS ON A TOPOLOGICAL RING
... (i) The operations of addition and product in Bbtb (X) are continuous with respect to the topology of uniform convergence on bounded sets; (ii) The operations of addition and product in Btbtb (X) are continuous with respect to the topology of uniform convergence on bounded sets; (iii) The operations ...
... (i) The operations of addition and product in Bbtb (X) are continuous with respect to the topology of uniform convergence on bounded sets; (ii) The operations of addition and product in Btbtb (X) are continuous with respect to the topology of uniform convergence on bounded sets; (iii) The operations ...
topology - DDE, MDU, Rohtak
... (iv) Since A ⊆ A ∪ B and B ⊆ A ∪ B d(A) ⊆ d (A ∪ B) and d(B) ⊆ d(A ∪ B) d(A) ∪ d(B) ⊆ d(A ∪ B) Conversely suppose that x ∉ d(A) ∪ d(B) and so x ∉ d(A) and x ∉ d(B). Therefore by definition, there must exist GA and GB containing x such that GA ∩ A − {x} = φ GB ∩ B − {x} = φ Let G = GA ∩ BB. By axiom ...
... (iv) Since A ⊆ A ∪ B and B ⊆ A ∪ B d(A) ⊆ d (A ∪ B) and d(B) ⊆ d(A ∪ B) d(A) ∪ d(B) ⊆ d(A ∪ B) Conversely suppose that x ∉ d(A) ∪ d(B) and so x ∉ d(A) and x ∉ d(B). Therefore by definition, there must exist GA and GB containing x such that GA ∩ A − {x} = φ GB ∩ B − {x} = φ Let G = GA ∩ BB. By axiom ...
Combinatorial Maps - People
... partially order by inclusion. A class of combinatorial maps, called ordered maps, includes the polytopes and most other classical examples, and it is shown that these are characterized by a linear diagram. The incidence structure S(G) generalizes the facial structure of a polytope. The examples that ...
... partially order by inclusion. A class of combinatorial maps, called ordered maps, includes the polytopes and most other classical examples, and it is shown that these are characterized by a linear diagram. The incidence structure S(G) generalizes the facial structure of a polytope. The examples that ...