On bornological products
نویسندگان
چکیده
منابع مشابه
Bornological Quantum Groups
We introduce and study the concept of a bornological quantum group. This generalizes the theory of algebraic quantum groups in the sense of van Daele from the algebraic setting to the framework of bornological vector spaces. Working with bornological vector spaces, the scope of the latter theory can be extended considerably. In particular, the bornological theory covers smooth convolution algeb...
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Bornological universes were introduced by Hu in [11] and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory. In [11] and [12] Hu gives a necessary and sufficient condition for which a bornological universe is metrizable. In this article we will give a characterization of uniformizable bornological universes. Furthermore, a cons...
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For non-metrizable spaces the classical Hausdorff dimension is meaningless. We extend the notion of Hausdorff dimension to arbitrary locally convex linear topological spaces, and thus to a large class of non-metrizable spaces. This involves a limiting procedure using the canonical bornological structure. In the case of normed spaces the new notion of Hausdorff dimension is equivalent to the cla...
متن کاملLocally Lipschitz Functions and Bornological Derivatives
We study the relationships between Gateaux, Weak Hadamard and Fréchet differentiability and their bornologies for Lipschitz and for convex functions. AMS Subject Classification. Primary: 46A17, 46G05, 58C20. Secondary: 46B20.
متن کاملClosed Graph Theorems for Bornological Spaces
The aim of this paper is that of discussing closed graph theorems for bornological vector spaces in a self-contained way, hoping to make the subject more accessible to non-experts. We will see how to easily adapt classical arguments of functional analysis over R and C to deduce closed graph theorems for bornological vector spaces over any complete, non-trivially valued field, hence encompassing...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1970
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500000811