Locally compact multivector extensions |
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Authors: | Juan Perá n |
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Affiliation: | Departamento de Matemática Aplicada, UNED Ap. 60149, Madrid 28080, Spain |
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Abstract: | The aim of this paper is to develop a locally compact extension of an arbitrary normed space in such a way that the initial algebraic structure is prolonged in some sense. To obtain such an extension, we weaken vector space axioms allowing a set-valued addition and introduce in this scheme a topological structure, by means of a hypertopology, and a compatible proximity. Finally, the locally compact multivector extension appears as an ultrafilter space. We also provide a Young measure related interpretation of these extensions when the normed space is an Lp space. |
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Keywords: | Local compactifications Proximities Hypertopologies Young measures |
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