Isometric Isomorphisms between Normed Spaces

Isometric Isomorphisms of Measure Algebras

Almost Isometric Embedding between Metric Spaces

We investigate the relations of almost isometric embedding and of almost isometry between metric spaces. These relations have several appealing features. For example, all isomorphism types of countable dense subsets of R form exactly one almost-isometry class, and similarly with countable dense subsets of Uryson’s universal separable metric space U. We investigate geometric, set-theoretic and m...

Isometric Differentiable Functions on Real Normed Space1

From now on S, T ,W , Y denote real normed spaces, f , f1, f2 denote partial functions from S to T , Z denotes a subset of S, and i, n denote natural numbers. Now we state the propositions: (1) Let us consider a set X and functions I, f . Then (f X) · I = (f · I) I−1(X). (2) Let us consider real normed spaces S, T , a linear operator L from S into T , and points x, y of S. Then L(x)− L(y) = L(x...

NORMED HYPERVECTOR SPACES

The main purpose of this paper is to study normed hypervector spaces. We generalize some definitions such as basis, convexity, operator norm, closed set, Cauchy sequences, and continuity in such spaces and prove some theorems about them.

Isomorphisms between Spaces of Vector-valued Continuous Functions

A theorem due to Milutin [12] (see also [13]) asserts that for any two uncountable compact metric spaces Qt and Q2> t n e spaces of continuous real-valued functions C ^ ) and C(Q2) are linearly isomorphic. It immediately follows from consideration of tensor products that if X is any Banach space then QQ^X) and C(Q2;X) are isomorphic. The purpose of this paper is to show that this conclusion is ...