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No abstract uploaded!

In this note we generalize two theorems of Klee [9] and a result of Bair-Jongmans [7] about the true separation of two convex cones; afterwards, we introduce the notion of true separation for$n(n≧2)$convex sets and we extend our three first statements for$n$convex cones.

We show that under conditions of regularity, if$E′$is isomorphic to$F′$, then the spaces of homogeneous polynomials over$E$and$F$are isomorphic. Some subspaces of polynomials more closely related to the structure of dual spaces (weakly continuous, integral, extendible) are shown to be isomorphic in full generality.

It is known that, unlike the one dimensional case it is not possible to find an upper bound for the zeros of an entire map from$C$^{$n$}to$C$^{$n$},$n$≥2, in terms of the growth of the map. However, if we only consider the “non-degenerate” zeros, that is, the zeros where the jacobian is not “too small”, it becomes possible. We give a new proof of this fact.