Examples of new nonstandard hulls of topological vector spaces.
Résumé
In this paper, we construct new nonstandard hulls of topological vector spaces using convex subrings of $ {}^*\mathbb{R}$ (or $ {}^*\mathbb{C}$) and we show that such spaces are complete. Some examples of locally convex spaces are provided to illustrate our construction. Namely, we show that the new nonstandard hull of the space of polynomials is the algebra of Colombeau's entire holomorphic generalized functions. The proof is based on the existence of global representatives of entire generalized functions.