SEPARATED PRESHEAVES OF NORMED SPACES AND Ω-VALUED NORMS

摘要

This paper lays down the axioms of Ω-valued normed spaces and shows their invariance under the so-called tilde-construction. Important examples are given by separated presheaves of normed spaces and by probabilistic normed spaces. Finally, there exists a natural Ω-valued topologization of Ω-valued normed spaces which makes it possible to study continuous linear operators between them.