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1972•Transactions of the American Mathematical SocietyRequires access

The Nonstandard Theory of Topological Vector Spaces

C. Ward Henson, L. C. Moore

Open publisher page 21 citations

Abstract

In this paper the nonstandard theory of topological vector spaces is developed, with three main objectives: (1) creation of the basic nonstandard concepts and tools; (2) use of these tools to give nonstandard treatments of some major standard theorems; (3) construction of the nonstandard hull of an arbitrary topological vector space, and the beginning of the study of the class of spaces which results.

About this research paper

What this paper is about

In this paper the nonstandard theory of topological vector spaces is developed, with three main objectives: (1) creation of the basic nonstandard concepts and tools; (2) use of these tools to give nonstandard treatments of some major standard theorems; (3) construction of the nonstandard hull of an arbitrary topological vector space, and the beginning of the study of the class of spaces which results.

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OpenAlex reports 21 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper the nonstandard theory of topological vector spaces is developed, with three main objectives: (1) creation of the basic nonstandard concepts and tools; (2) use of these tools to give nonstandard treatments of some major standard theorems; (3) construction of the nonstandard hull of an arbitrary topological vector space, and the beginning of the study of the class of spaces which results.

Key concepts: Mathematics, Topological vector space, Topological space, Locally convex topological vector space, Topological tensor product, Vector space, Topology (electrical circuits), Class (philosophy)

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