Regular Closure Operators and Compactness
نویسنده
چکیده
Résumé. Une légère modification de la notion de compacité relativement à un opérateur de fermeture permet d’étendre à la catégorie TOP des espaces topologiques divers résultats sur les opérateurs de fermeture réguliers obtenus pour la catégorie AB des groups abéliens. Ainsi les épimorphismes dans les sous-catégories des objets compacts ou compactsséparés pour un opérateur de fermeture régulier additif sont surjectifs. L’auteur montre aussi que sous certaines conditions sur une sous-catégorie A de TOP, la sous-catégorie engendrée par les objets compacts-séparés pour l’opérateur de fermeture régulier induit sur A a plusieurs bonnes propriétés normalement obtenues dans des catégories algébriques.
منابع مشابه
New operators through measure of non-compactness
In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...
متن کاملCompactness, Perfectness, Separation, Minimality and Closedness with Respect to Closure Operators
In this paper, the characterization of closed and strongly closed subobjects of an object in categories of various types of filter convergence spaces is given and it is shown that they induce a notion of closure. Furthermore, each of the notions of compactness, perfectness, separation, minimality and absolute closedness with respect to these two new closure operators are characterized in these ...
متن کاملWhen strict singularity of operators coincides with weak compactness
We prove that the notions of finite strict singularity, strict singularity and weak compactness coincide for operators defined on various spaces: the disc algebra, subspaces of C(K) with reflexive annihilator and subspaces of the Morse-TransueOrlicz space Mq (Ω, μ) with q > 2.
متن کاملM-FUZZIFYING MATROIDS INDUCED BY M-FUZZIFYING CLOSURE OPERATORS
In this paper, the notion of closure operators of matroids is generalized to fuzzy setting which is called $M$-fuzzifying closure operators, and some properties of $M$-fuzzifying closure operators are discussed. The $M$-fuzzifying matroid induced by an $M$-fuzzifying closure operator can induce an $M$-fuzzifying closure operator. Finally, the characterizations of $M$-fuzzifying acyclic matroi...
متن کاملBilateral composition operators on vector-valued Hardy spaces
Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$. We investigate some operator theoretic properties of bilateral composition operator $C_{ph, T}: f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq +infty$. Compactness and weak compactness of $C_{ph, T}$ on $H^p(X)$ are characterized an...
متن کاملEmbedding Operators and Maximal Regular Differential-operator Equations in Banach-valued Function Spaces
This study focuses on anisotropic Sobolev type spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E, depending of α and order of spaces are found that ...
متن کامل