共查询到20条相似文献,搜索用时 15 毫秒
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We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of retractions of a certain kind. Consequently, a compact space of weight?ℵ1 is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight?ℵ1 is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors. 相似文献
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《Indagationes Mathematicae (Proceedings)》1982,85(4):423-439
Nuclearity of certain classes of non-archimedean Frechet spaces and their dual spaces is studied. 相似文献
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Ondej F.K. Kalenda 《Journal of Mathematical Analysis and Applications》2009,350(2):464-484
We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L1 spaces, Banach lattices and noncommutative L1 spaces. 相似文献
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Ond?ej F.K. Kalenda 《Journal of Mathematical Analysis and Applications》2008,340(1):81-101
We collect examples of Valdivia compact spaces, their continuous images and associated classes of Banach spaces which appear naturally in various branches of mathematics. We focus on topological constructions generating Valdivia compact spaces, linearly ordered compact spaces, compact groups, L1 spaces, Banach lattices and noncommutative L1 spaces. 相似文献
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T Sengadir 《Proceedings Mathematical Sciences》2007,117(1):71-84
In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We
choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence
and uniqueness of solutions. 相似文献
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The aim of this note is to investigate the topological structure (in particular the density condition) of subspaces and separated quotients of Fréchet spaces. Our main result is the following one: LetE be a Fréchet space which is neither Montel nor isomorphic to a closed subspace ofX × , withX a Banach space, also assume thatE can be written asFG withF andG infinite dimensional closed subspaces ofE not isomorphic to , thenE contains a closed subspace with basis and not satisfying the density condition. We also prove that every Köthe echelon space of orderp, 1<p<, which is not quasinormable has a separated quotient with basis which does not satisfy the density condition. 相似文献
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J.C. Ferrando 《Journal of Mathematical Analysis and Applications》2006,324(2):862-881
Valdivia invented a nondistinguished Fréchet space whose weak bidual is quasi-Suslin but not K-analytic. We prove that Grothendieck/Köthe's original nondistinguished Fréchet space serves the same purpose. Indeed, a Fréchet space is distinguished if and only if its strong dual has countable tightness, a corollary to the fact that a (DF)-space is quasibarrelled if and only if its tightness is countable. This answers a Cascales/K?kol/Saxon question and leads to a rich supply of (DF)-spaces whose weak duals are quasi-Suslin but not K-analytic, including the spaces Cc(κ) for κ a cardinal of uncountable cofinality. Our level of generality rises above (DF)- or even dual metric spaces to Cascales/Orihuela's class G. The small cardinals b and d invite a novel analysis of the Grothendieck/Köthe example, and are useful throughout. 相似文献
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Mark Finkelstein Howard G. Tucker Jerry Alan Veeh 《Proceedings of the American Mathematical Society》1999,127(9):2773-2777
The existence, uniqueness, and convergence properties of distinguished logarithms of multivariate characteristic functions are proved.
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