On Infinitesimal L_ω-smooth Functions.

Abstract

The aim of this paper is to study smoothness, approximate continuity, and approximate derivative in a nonstandard manner with respect to infinitesimal parameters. The new nonstandard introduced definitions are combined with standard and nonstandard intermediate value property. Particularly, we show that the existence  of continuous and smooth function has the infinitesimal intermediate value property. Moreover, for the same result, we reduce the continuity condition to the infinitesimal intermediate value condition

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