Separated Presheaves of Normed Spaces and -valued Norms

Abstract

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

Fuzzy sets and sheaves. Part I

“…Then there exists a unique separated -valued equality E F on A F provided with the following properties (cf. [28]): F (a, a) = , a ∈ F( ).…”