The notion of ultrametrics can be considered as a zero-dimensional analogue ordinary metrics, and it is expected to prove ultrametric versions theorems on metric spaces. In this paper, we provide the Arens-Eells isometric embedding theorem spaces, Hausdorff extension Niemytzki-Tychonoff characterization compactness, author’s interpolation metrics dense subsets spaces metrics.

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on  a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of  level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity...

We prove that all Arens extensions of finite rank Riesz multimorphisms taking values in Archimedean spaces coincide and are multimorphisms. also that, for a class Banach lattices F, which includes F=c0,ℓp,c0(ℓp),ℓp(c0), ℓp(ℓs),1<p,s<∞, among many others, Aron-Berner any F-valued multimorphism between