# Sh:827

- Kojman, M., & Shelah, S. (2006).
*Almost isometric embedding between metric spaces*. Israel J. Math.,**155**, 309–334. arXiv: math/0406530 DOI: 10.1007/BF02773958 MR: 2269433 -
Abstract:

We investigate a relations of*almost isometric embedding*and*almost isometry*between metric spaces and prove that with respect to these relations:(1) There is a countable universal metric space.

(2) There may exist fewer than continuum separable metric spaces on \aleph_1 so that every separable metric space is almost isometrically embedded into one of them when the continuum hypothesis fails.

(3) There is no collection of fewer than continuum metric spaces of cardinality \aleph_2 so that every ultra-metric space of cardinality \aleph_2 is almost isometrically embedded into one of them if \aleph_2<2^{\aleph_0}.

We also prove that various spaces X satisfy that if a space X is almost isometric to X than Y is isometric to X.

- published version (26p)

Bib entry

@article{Sh:827, author = {Kojman, Menachem and Shelah, Saharon}, title = {{Almost isometric embedding between metric spaces}}, journal = {Israel J. Math.}, fjournal = {Israel Journal of Mathematics}, volume = {155}, year = {2006}, pages = {309--334}, issn = {0021-2172}, doi = {10.1007/BF02773958}, mrclass = {54E35 (03E05 03E35 54A35)}, mrnumber = {2269433}, mrreviewer = {Klaas Pieter Hart}, doi = {10.1007/BF02773958}, note = {\href{https://arxiv.org/abs/math/0406530}{arXiv: math/0406530}}, arxiv_number = {math/0406530} }