It is known that the dierent stages of the Cartan-Whitehead decomposition of a 0-connected space ... more It is known that the dierent stages of the Cartan-Whitehead decomposition of a 0-connected space can be obtained as the Adams cocompletions of the space with respect to suitable sets of morphisms. In this note Cartan-Whitehead decomposition is obtained for a nilpotent space, in terms of Adams cocompletion, using the primary homotopy theory developed by Neisendonfer.
Cayley's Theorem states that a permutation group of a group is isomorphic to the given group. We ... more Cayley's Theorem states that a permutation group of a group is isomorphic to the given group. We show that this permutation group is Adams completion of the group with respect to a suitably chosen set of morphisms in the category of groups and homomorphisms.
By introducing fuzzy upper and lower correspondence between fuzzy topological spaces, the fuzzy v... more By introducing fuzzy upper and lower correspondence between fuzzy topological spaces, the fuzzy version of the topological intersection theorem is proved.
The concepts of fuzzy products and their duals, namely, fuzzy coproducts are already known for fu... more The concepts of fuzzy products and their duals, namely, fuzzy coproducts are already known for fuzzy topological spaces. In this paper the concepts of fuzzy equalizers and fuzzy pullbacks and their duals, namely, fuzzy coequalizers and fuzzy pushouts are introduced for fuzzy topological spaces and various results concerning fuzzy products, fuzzy equalizers and fuzzy pullbacks and their duals are explored.
International Journal of Mathematics and Mathematical Sciences, 2006
The concept ofη-invex set is explored and the concept ofT-η-invex function is introduced. These c... more The concept ofη-invex set is explored and the concept ofT-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces. The study of variational inequality problems is extended toH-spaces and differentiablen-manifolds. The solution of complementarity problem is also studied in the presence of fixed points or Lefschetz number.
Journal of the Australian Mathematical Society, 1987
Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categoric... more Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, the Adams cocompletion of an object in a category. In this paper the different stages of the Cartan-Whitehead decomposition of a O-connected space are shown to be the cocompletions of the space with respect to suitable sets of morphisms.
Under a set of conditions, it is shown that the Kan extension of an additive homology theory over... more Under a set of conditions, it is shown that the Kan extension of an additive homology theory over smaller admissible subcategory is again a homology theory. Furthermore, using a Serre class of abelian groups, it is shown that a homology theory over the category of simply connected based topological spaces and continuous maps arising through Kan extension process from an additive homology theory over a smaller subcategory always admits global Adams cocompletion. 1.
The concept of fuzzy compact-open topology is introduced and some characterizations of this topol... more The concept of fuzzy compact-open topology is introduced and some characterizations of this topology are discussed.
MATTER: International Journal of Science and Technology
Under a reasonable assumption, the minimal model of a 1-connected d.g.a. can be expressed as the ... more Under a reasonable assumption, the minimal model of a 1-connected d.g.a. can be expressed as the Adams cocompletion of the d.g.a. with respect to a chosen set of d.g.a.-maps.
Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categori... more Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.
Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categoric... more Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context. In this note, it is shown that given an algebra, its exterior algebra is isomorphic to the Adams completion of the algebra with respect to a chosen set of morphisms in a suitable category.
The concepts of h-limits, strong h-limits (and their duals) and partial proofs of homotopy limit ... more The concepts of h-limits, strong h-limits (and their duals) and partial proofs of homotopy limit reduction theorems relating to h-limits and strong h-limits are already known for a groupoid enriched category (g.e. category). In this paper the concepts of weak h-limits, quasi-limits (and their duals) are introduced in a g.e. category and the fuller version of the homotopy limit reduction theorems concerning the four types of limits, i.e., weak h-limits, h-limits, strong h-limits and quasi-limits are proved. The previously called Brown Complement Theorem is proved under the restricted assumption that the g.e. category admits only weak h-limits instead of h-limits and the generalized version of the Brown Complement Theorem is also proved which is relevant to the problem of showing under suitable smallness conditions that if a g.e. category admits all h-limits then it also admits all h-colomits.
It is known that the dierent stages of the Cartan-Whitehead decomposition of a 0-connected space ... more It is known that the dierent stages of the Cartan-Whitehead decomposition of a 0-connected space can be obtained as the Adams cocompletions of the space with respect to suitable sets of morphisms. In this note Cartan-Whitehead decomposition is obtained for a nilpotent space, in terms of Adams cocompletion, using the primary homotopy theory developed by Neisendonfer.
Cayley's Theorem states that a permutation group of a group is isomorphic to the given group. We ... more Cayley's Theorem states that a permutation group of a group is isomorphic to the given group. We show that this permutation group is Adams completion of the group with respect to a suitably chosen set of morphisms in the category of groups and homomorphisms.
By introducing fuzzy upper and lower correspondence between fuzzy topological spaces, the fuzzy v... more By introducing fuzzy upper and lower correspondence between fuzzy topological spaces, the fuzzy version of the topological intersection theorem is proved.
The concepts of fuzzy products and their duals, namely, fuzzy coproducts are already known for fu... more The concepts of fuzzy products and their duals, namely, fuzzy coproducts are already known for fuzzy topological spaces. In this paper the concepts of fuzzy equalizers and fuzzy pullbacks and their duals, namely, fuzzy coequalizers and fuzzy pushouts are introduced for fuzzy topological spaces and various results concerning fuzzy products, fuzzy equalizers and fuzzy pullbacks and their duals are explored.
International Journal of Mathematics and Mathematical Sciences, 2006
The concept ofη-invex set is explored and the concept ofT-η-invex function is introduced. These c... more The concept ofη-invex set is explored and the concept ofT-η-invex function is introduced. These concepts are applied to the generalized vector variational inequality problems in ordered topological vector spaces. The study of variational inequality problems is extended toH-spaces and differentiablen-manifolds. The solution of complementarity problem is also studied in the presence of fixed points or Lefschetz number.
Journal of the Australian Mathematical Society, 1987
Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categoric... more Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context; they have also suggested the dual notion, namely, the Adams cocompletion of an object in a category. In this paper the different stages of the Cartan-Whitehead decomposition of a O-connected space are shown to be the cocompletions of the space with respect to suitable sets of morphisms.
Under a set of conditions, it is shown that the Kan extension of an additive homology theory over... more Under a set of conditions, it is shown that the Kan extension of an additive homology theory over smaller admissible subcategory is again a homology theory. Furthermore, using a Serre class of abelian groups, it is shown that a homology theory over the category of simply connected based topological spaces and continuous maps arising through Kan extension process from an additive homology theory over a smaller subcategory always admits global Adams cocompletion. 1.
The concept of fuzzy compact-open topology is introduced and some characterizations of this topol... more The concept of fuzzy compact-open topology is introduced and some characterizations of this topology are discussed.
MATTER: International Journal of Science and Technology
Under a reasonable assumption, the minimal model of a 1-connected d.g.a. can be expressed as the ... more Under a reasonable assumption, the minimal model of a 1-connected d.g.a. can be expressed as the Adams cocompletion of the d.g.a. with respect to a chosen set of d.g.a.-maps.
Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categori... more Deleanu, Frei, and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, we have obtained the Postnikov-like approximation of a module, with the help of a suitable set of morphisms.
Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categoric... more Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context. In this note, it is shown that given an algebra, its exterior algebra is isomorphic to the Adams completion of the algebra with respect to a chosen set of morphisms in a suitable category.
The concepts of h-limits, strong h-limits (and their duals) and partial proofs of homotopy limit ... more The concepts of h-limits, strong h-limits (and their duals) and partial proofs of homotopy limit reduction theorems relating to h-limits and strong h-limits are already known for a groupoid enriched category (g.e. category). In this paper the concepts of weak h-limits, quasi-limits (and their duals) are introduced in a g.e. category and the fuller version of the homotopy limit reduction theorems concerning the four types of limits, i.e., weak h-limits, h-limits, strong h-limits and quasi-limits are proved. The previously called Brown Complement Theorem is proved under the restricted assumption that the g.e. category admits only weak h-limits instead of h-limits and the generalized version of the Brown Complement Theorem is also proved which is relevant to the problem of showing under suitable smallness conditions that if a g.e. category admits all h-limits then it also admits all h-colomits.
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Papers by Akrur Behera