Abstract
Definition 1. — Given a topological division ring K (GT, III, § 6.7) and a set E such that E has
-
1°
the structure of a left vector space on K;
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2°
a topology compatible with the structure of the additive group of E (GT, III, §1.1) and satisfying in addition the following axiom:
(EVT) the mapping (λ, x) ↦ λx of K × E in E is continuous, then E is called a left topological vector space over (or on) K.
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© 2003 Springer-Verlag Berlin Heidelberg
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Bourbaki, N. (2003). Topological vector spaces over a valued division ring. In: Topological Vector Spaces. Elements of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61715-7_1
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DOI: https://doi.org/10.1007/978-3-642-61715-7_1
Publisher Name: Springer, Berlin, Heidelberg
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