On paratopological vector spaces |
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Authors: | Carmen Alegre Salvador Romaguera |
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Institution: | (1) E. U. Informática, Departamento De Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain;(2) Escuela de Caminos, Departamento De Matemática Aplicada, Universidad Politécnica de Valencia, 46071 Valencia, Spain |
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Abstract: | We show that each first countable paratopological vector space X has a compatible translation invariant quasi-metric such that the open balls are convex whenever X is a pseudoconvex vector space. We introduce the notions of a right-bounded subset and of a right-precompact subset of a
paratopological vector space X and prove that X is quasi-normable if and only if the origin has a convex and right-bounded neighborhood. Duality in this context is also
discussed. Furthermore, it is shown that the bicompletion of any paratopological vector space (respectively, of any quasi-metric
vector space) admits the structure of a paratopological vector space (respectively, of a quasi-metric vector space). Finally,
paratopological vector spaces of finite dimension are considered.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | translation invariant quasi-metric paratopological vector space quasi-norm continuous linear map right-bounded bicompletion pseudoconvex paratopological group |
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