Tight span of subsets of the plane with the maximum metric

Kilic M., Kocak S.

ADVANCES IN MATHEMATICS, cilt.301, ss.693-710, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 301
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.aim.2016.05.026
  • Dergi Adı: ADVANCES IN MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.693-710
  • Anahtar Kelimeler: Tight span, Hyperconvexity, Injective envelope, Manhattan plane, OPTIMAL REALIZATIONS, SPACES
  • Anadolu Üniversitesi Adresli: Evet

Özet

We prove that a nonempty closed and geodesically convex subset of the l(infinity) plane R-infinity(2) is hyperconvex and we characterize the tight spans of arbitrary subsets of R-infinity(2) via this property: Given any nonempty X subset of R-infinity(2), a closed, geodesically convex and minimal subset Y subset of R-infinity(2) containing X is isometric to the tight span T(X) of X. (C) 2016 Elsevier Inc. All rights reserved.