caa a22 4500 469068345 CHVBK 20180323132914.0 cr unu---uuuuu 170328e19920201xx s 000 0 eng 10.1007/BF02764804 doi (NATIONALLICENCE)springer-10.1007/BF02764804 Finite metric spaces needing high dimension for lipschitz embeddings in banach spaces [Elektronische Daten] [Juan Arias-de-Reyna, Luis Rodríguez-Piazza] We construct a sequence of metric spaces (M n) with cardM n=3n satisfying that for everyc<2, there exists a real numbera(c)>0 such that, if the Lipschitz distance fromM n to a subset of a Banach spaceE is less thanc, then dim(E) ≥a(c)n. We also prove several results about embeddings of metric spaces whose non-zero distance values are in the interval [1,2]. The Magnes Press, 1992 Arias-de-Reyna Juan Departmento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080, Sevilla, Spain aut Rodríguez-Piazza Luis Departmento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080, Sevilla, Spain aut Israel Journal of Mathematics Springer-Verlag 79/1(1992-02-01), 103-111 0021-2172 79:1<103 1992 79 11856 https://doi.org/10.1007/BF02764804 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02764804 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Arias-de-Reyna Juan Departmento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080, Sevilla, Spain aut NATIONALLICENCE 700 1- Rodríguez-Piazza Luis Departmento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, 41080, Sevilla, Spain aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer-Verlag 79/1(1992-02-01), 103-111 0021-2172 79:1<103 1992 79 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer