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... exists a preopen set ρ in X containing xε such that f (ρ) ≤ β. Therefore, we obtain yν ∈ µ and f (ρ) ∧ µ = ∅. This shows that G(f ) is fuzzy pre-co-closed. Theorem 28. If f : X → Y is fuzzy precontinuous and Y is fuzzy co-T1 , then G(f ) is fuzzy pre-co-closed in X × Y . Proof. Let (xε , yν ) ∈ (X × ...

... exists a preopen set ρ in X containing xε such that f (ρ) ≤ β. Therefore, we obtain yν ∈ µ and f (ρ) ∧ µ = ∅. This shows that G(f ) is fuzzy pre-co-closed. Theorem 28. If f : X → Y is fuzzy precontinuous and Y is fuzzy co-T1 , then G(f ) is fuzzy pre-co-closed in X × Y . Proof. Let (xε , yν ) ∈ (X × ...

View PDF - Journal of Computer and Mathematical Sciences

... spaces, European Journal of Pure and Applied Mathematics, Vol 3, No.2,295-302 (2010). 10. S. Sekar and J. Jayakumar, On supra I-open sets and Supra I continuous functions, International journal of Scientific and Engineering Research, Volume 3, Issue 5, May (2012). 11. D. Singh, Almost perfectly cont ...

... spaces, European Journal of Pure and Applied Mathematics, Vol 3, No.2,295-302 (2010). 10. S. Sekar and J. Jayakumar, On supra I-open sets and Supra I continuous functions, International journal of Scientific and Engineering Research, Volume 3, Issue 5, May (2012). 11. D. Singh, Almost perfectly cont ...

About dual cube theorems

... the sense of Quillen [9]. Such categories (when pointed) have been shown to be the right place to build the theory of LS-category of their objects (spaces, simplicial sets, differential graded algebras, differential graded Lie algebras, etc.), provided an additional axiom holds: Axiom 2 in this pape ...

... the sense of Quillen [9]. Such categories (when pointed) have been shown to be the right place to build the theory of LS-category of their objects (spaces, simplicial sets, differential graded algebras, differential graded Lie algebras, etc.), provided an additional axiom holds: Axiom 2 in this pape ...

Posets and homotopy

... We may therefore identify a poset P with its associated A-space X (P ). The homotopy type of P is the homotopy type of X (P ). McCord (1966) shows that K(P ) and P have the same weak homotopy type. More specifically, there is a weak homotopy equivalence f : |K(P )| → P . For a simplicial complex K , ...

... We may therefore identify a poset P with its associated A-space X (P ). The homotopy type of P is the homotopy type of X (P ). McCord (1966) shows that K(P ) and P have the same weak homotopy type. More specifically, there is a weak homotopy equivalence f : |K(P )| → P . For a simplicial complex K , ...

Simplicial sets

... difficulty is that the cartesian product of two simplices of positive dimension is not a simplex. As a consequence, there is no natural operation of a cartesian product on simplicial complexes. Finally, there is no notion of a quotient simplicial complex, which would be necessary for many constructi ...

... difficulty is that the cartesian product of two simplices of positive dimension is not a simplex. As a consequence, there is no natural operation of a cartesian product on simplicial complexes. Finally, there is no notion of a quotient simplicial complex, which would be necessary for many constructi ...

Lecture Notes on Smale Spaces

... Notice that if [y, x] is the intersection of Ey and Fx , saying that it is equal to x simply says that x is in Ey . Although it is not stated in the heuristic definition, this should also mean that y is in Ex . So the hypothesis of C1 above is really that y and z are both in Ex . With this in mind, ...

... Notice that if [y, x] is the intersection of Ey and Fx , saying that it is equal to x simply says that x is in Ey . Although it is not stated in the heuristic definition, this should also mean that y is in Ex . So the hypothesis of C1 above is really that y and z are both in Ex . With this in mind, ...

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 ...

ON A GENERALIZATION OF SLIGHT CONTINUITY

... The complement of a preopen set is said to be preclosed [5]. The complement of a δ-preopen set is said to be δ-preclosed. The intersection of all δ-preclosed sets of X containing A is called the δ-preclosure [12] of A and is denoted by δ-pcl(A). The union of all δ-preopen sets of X contained A is ca ...

... The complement of a preopen set is said to be preclosed [5]. The complement of a δ-preopen set is said to be δ-preclosed. The intersection of all δ-preclosed sets of X containing A is called the δ-preclosure [12] of A and is denoted by δ-pcl(A). The union of all δ-preopen sets of X contained A is ca ...

SOME RESULTS ON CONNECTED AND MONOTONE FUNCTIONS

... f −1 (B) is a singleton because X is biconnected. Hence, either A or B is a singleton and therefore the result follows. Conversely, suppose Y is biconnected and let A, B be two disjoint connected subsets of X, with X = A ∪ B. Then f (A) and f (B) are two disjoint connected subsets of Y, with Y = f ( ...

... f −1 (B) is a singleton because X is biconnected. Hence, either A or B is a singleton and therefore the result follows. Conversely, suppose Y is biconnected and let A, B be two disjoint connected subsets of X, with X = A ∪ B. Then f (A) and f (B) are two disjoint connected subsets of Y, with Y = f ( ...

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 ...

Simplicial Sets - Stanford Computer Graphics

... Homology of Simplicial Set • Chain complexes are the free abelian groups on the n-simplices • Boundary operator: (-1)i di • Degenerate (x = si y) complexes are 0 • Homology of Simplicial Set is the same as the homology of the simplicial complex ...

... Homology of Simplicial Set • Chain complexes are the free abelian groups on the n-simplices • Boundary operator: (-1)i di • Degenerate (x = si y) complexes are 0 • Homology of Simplicial Set is the same as the homology of the simplicial complex ...

Connectedness and continuity in digital spaces with the Khalimsky

... What is a digital space? The word digital comes from the Latin digitus, meaning ’finger, toe’. The herb purple foxglove, has flowers that look like a bunch of fingers (or gloves rather). In Latin it is called Digitalis purpurea. This herb is the source of a medicine, Digitalis 1 , that is still toda ...

... What is a digital space? The word digital comes from the Latin digitus, meaning ’finger, toe’. The herb purple foxglove, has flowers that look like a bunch of fingers (or gloves rather). In Latin it is called Digitalis purpurea. This herb is the source of a medicine, Digitalis 1 , that is still toda ...

Italo Jose Dejter (Bahia Blanca, 1939) is an Argentine-born American mathematician of Bessarabian Jewish descent. He is a professor at the University of Puerto Rico (UPRRP) since 1984 and has conducted research in mathematics, particularly in areas that include algebraic topology, differential topology, graph theory, coding theory and design theory.He has an Erdos number of 2 since 1993.Dejter completed the Licentiate degree in Mathematics from University of Buenos Aires in 1967, and the Ph.D. degree in Mathematics from Rutgers University in 1975 under the supervision of Ted Petrie. He was a professor atFederal University of Santa Catarina, Brazil, from 1977 to 1984. Dejter has been a visiting scholar at a number of research institutions, including University of São Paulo,Instituto Nacional de Matemática Pura e Aplicada, Federal University of Rio Grande do Sul,University of Cambridge,National Autonomous University of Mexico, Simon Fraser University, University of Victoria, New York University, University of Illinois at Urbana–Champaign, McMaster University,DIMACS, Autonomous University of Barcelona, Technical University of Denmark, Auburn University, Polytechnic University of Catalonia, Technical University of Madrid, Charles University, Ottawa University, Simón Bolívar University, etc. The sections below describe the relevance of Dejter's work in the research areas mentioned in the first paragraph above, or in the box to the right.