Extending partial isometries of generalized metric spaces

Extending Partial Isometries

We show that a finite metric space A admits an extension to a finite metric space B so that each partial isometry of A extends to an isometry of B. We also prove a more precise result on extending a single partial isometry of a finite metric space. Both these results have consequences for the structure of the isometry groups of the rational Urysohn metric space and the Urysohn metric space.

Partial Isometries on Banach Spaces

Local Isometries of Compact Metric Spaces

By local isometries we mean mappings which locally preserve distances. A few of the main results are: 1. For each local isometry / of a compact metric space (M,p) into itself there exists a unique decomposition of M into disjoint open sets, M = Ai g U • • • U Ai>, (0 < n < oo) such that (i) f(M}0) = M!Q, and (ii) f(M{) C M{_x and M< ^ 0 for each i, 1 < i < n. 2. Each local isometry of a metric ...

Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space

We prove the equivalence of the two important facts about finite metric spaces and universal Urysohn metric spaces U, namely theorem A and theorem B below: Theorem A (Approximation): The group of isometry ISO(U) contains everywhere dense locally finite subgroup; Theorem G(Globalization): For each finite metric space F there exists another finite metric space F̄ and isometric imbedding j of F to ...

FORMAL BALLS IN FUZZY PARTIAL METRIC SPACES

In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.