A THEOREM OF TYPE "PARTITION OF UNITY" WITH APPLICATIONS IN THE WEIGHTED SPACES.

In the first part of the paper, we present a theorem of type "partition of unity", and three of its consequences, i.e., for algebras, linear subspaces and convex cones. In the second part, some theorems of localizability (or density) in a weighted space are presented. We mention that the weighted spaces are classes of continuous scalar functions on a locally compact space (for example, the space of function with compact support, the space of bounded functions, the space of functions vanishing at infinity, the space of functions rapidly decreasing at infinity). [ABSTRACT FROM AUTHOR]