Olijnyk B. Isomorphic embeddings and Gromov-Hausdorff metric of finite metric spaces

Isomorphic embeddings of finite metric spaces and properties of Gromov-Hausdorff distance between finite metric spaces are investigated. A construction of isomorphic embedding of arbitrary finite metric space into some Hamming space is presented and an algorithm of such embedding is described. A continuum family of such pairwise non-isomorphic homogenous locally finite metric spaces, that each of them contains an isomorphic copy of arbitrary finite metric space, is constructed. A Gromov-Hausdorff exponent of finite metric space is defined, some of its properties are investigated.