The nonstandard theory of topological vector spaces

Henson, C. Ward; Moore, L. C.

doi:10.1090/S0002-9947-1972-0308722-5

The nonstandard theory of topological vector spaces
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by C. Ward Henson and L. C. Moore PDF

Trans. Amer. Math. Soc. 172 (1972), 405-435 Request permission

Erratum: Trans. Amer. Math. Soc. 184 (1973), 509.

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.

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On some criteria for the regularity of spaces of the type

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