Tight span of subsets of the plane with the maximum metric

Kilic M., Kocak S.

ADVANCES IN MATHEMATICS, vol.301, pp.693-710, 2016 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 301
  • Publication Date: 2016
  • Doi Number: 10.1016/j.aim.2016.05.026
  • Journal Name: ADVANCES IN MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.693-710
  • Keywords: Tight span, Hyperconvexity, Injective envelope, Manhattan plane, OPTIMAL REALIZATIONS, SPACES
  • Anadolu University Affiliated: Yes

Abstract

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.