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Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by $K^{0}$ the set of all X ∈ K() such that the farthest distance mapping $a \mapsto M_{X} (a)$ is multivalued on a dense subset of . It is proved that $K^{0}$ is a residual dense subset of K().

An O(n log n) Algorithm for the All-Nearest-Neighbors Problem.

P.M. Vaidya (1989)

Discrete & computational geometry

Approximating Euclidean Distances by Small Degree Graphs*

José Soares (1994)

Discrete & computational geometry

Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics

Wladimir G. Boskoff, Bogdan D. Suceavă (2008)

Czechoslovak Mathematical Journal

In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian's metrization procedure can be relaxed. Then, we prove that Barbilian's metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.

Block distance matrices.

Balaji, R., Bapat, R.B. (2007)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Calcul du rayon de la sphère inscrite dans le tétraèdre

Georges Dostor (1873)

Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale

Classification of six-point metrics.

Sturmfels, Bernd, Yu, Josephine (2004)

The Electronic Journal of Combinatorics [electronic only]

Diameter-Extremal Subsets of Spheres.

M. Katz (1989)

Discrete & computational geometry

Distance-preserving maps in generalized polygons. I: Maps on flags.

Govaert, Eline, Van Maldeghem, Hendrik (2002)

Beiträge zur Algebra und Geometrie

Dividing an arc to subarcs with equal chords

Jussi Väisälä (1982)

Colloquium Mathematicae

Einbettung endlicher metrischer Räume

M. Richter (1986)

Beiträge zur Algebra und Geometrie = Contributions to algebra and geometry

Euclidean and circum-Euclidean distance matrices: characterizations and linear preservers.

Li, Chi-Kwong, Milligan, Thomas, Trosset, Michael W. (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Geometry without topology as a new conception of geometry.

Rylov, Yuri A. (2002)

International Journal of Mathematics and Mathematical Sciences

Homogeneity properties of hypercubes.

O. Ovchinnikov (2007)

Mathware and Soft Computing

Hyperconvexity of ℝ-trees

W. Kirk (1998)

Fundamenta Mathematicae

It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.

Isometries on linear $n$ -normed spaces.

Park, Chun-Gil, Rassias, Themistocles M. (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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