On the way to Frölicher bornology

Abstract

In this work we introduce the concept of bornology on the theory of Frölicher spaces. A canonical bornology, called the functional bornology, is induced from structure functions, and bounded maps under this bornology are determined. Based on the structure of structure curves, we deduce that we cannot induce, canonically, a bornology from structure curves. For each of Frölicher subspace and product, an initial and functional bornology are induced and compared. Similarly, for each of Frölicher quotient and coproduct, a final and functional bornology are induced and compared.