Let K=(K,v,…) be a dp-minimal expansion of non-trivially valued field characteristic 0 and F an infinite interpretable in K. Assume that K is one the following: (i) V-minimal, (ii) power bounded T-convex, or (iii) P-minimal (assuming additionally generic differentiability definable functions). Then definably isomorphic to finite extension or, cases (ii), its residue field. In particular, every ...

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.