caa a22 4500 469075023 CHVBK 20180323132933.0 cr unu---uuuuu 170328e19921201xx s 000 0 eng 10.1007/BF02293054 doi (NATIONALLICENCE)springer-10.1007/BF02293054 A bounded compactness theorem for L 1-embeddability of metric spaces in the plane [Elektronische Daten] [Seth Malitz, Jerome Malitz] LetM=(W, d) be a metric space. LetL 1 denote theL 1 metric. AnL 1-embedding ofM into Cartesiank-space ℝ k is a distance-preserving map from (W, d) into (ℝ k ,L 1). Letc(k) be the smallest integer such that for every metric spaceM, M isL 1-embeddable inR k iff everyc(k)-sized subspace ofM isL 1-embeddable inR k. A special case of a theorem of Menger (see p. 94 of [5]) says thatc(1) exists and equals 4. We show thatc(2) exists and satisfies 6≦c(2)≦11. Whether or notc(k) exists for anyk≧3 is an open question. Springer-Verlag New York Inc., 1992 Malitz Seth Department of Computer Science, University of Massachusetts, 01003, Amherst, MA, USA aut Malitz Jerome Department of Mathematics, University of Colorado, 80309, Boulder, CO, USA aut Discrete & Computational Geometry Springer New York 8/4(1992-12-01), 373-385 0179-5376 8:4<373 1992 8 454 https://doi.org/10.1007/BF02293054 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02293054 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Malitz Seth Department of Computer Science, University of Massachusetts, 01003, Amherst, MA, USA aut NATIONALLICENCE 700 1- Malitz Jerome Department of Mathematics, University of Colorado, 80309, Boulder, CO, USA aut NATIONALLICENCE 773 0- Discrete & Computational Geometry Springer New York 8/4(1992-12-01), 373-385 0179-5376 8:4<373 1992 8 454 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer