Geodesic
On the Nonstandard Duality Theory of Locally Convex Spaces
Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 460-479

Voir la notice de l'article provenant de la source Cambridge University Press

This paper continues the nonstandard duality theory of locally convex, topological vector spaces begun in Section 5 of [3]. In Section 1, we isolate an external property, called the pseudo monad, that appears to be one of the central concepts of the theory (Definition 1.2). In Section 2, we relate the pseudo monad to the Fin operation. For example, it is shown that the pseudo monad of a μ-saturated subset A of *E, the nonstandard model of the vector space E, is the smallest subset of A that generates Fin (A) (Proposition 2.7).The nonstandard model of a dual system of vector spaces is considered in Section 3. In this section, we use pseudo monads to establish relationships among infinitesimal polars, finite polars (see (3.1) and (3.2)) and the Fin operation (Theorem 3.7). 
Grainger, Arthur D. On the Nonstandard Duality Theory of Locally Convex Spaces. Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 460-479. doi: 10.4153/CJM-1980-037-4
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