\((m, n)\)-equidistant sets in \(\mathbb{R}^{k},\mathbb{S}^{k}\), and \(\mathbb P^k\)

DOI10.1007/s00454-007-9048-4zbMath1158.54012OpenAlexW2017708783MaRDI QIDQ958223

Strashimir G. Popvassilev

Publication date: 2 December 2008

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-007-9048-4

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Distance geometry (51K99) Combinatorial geometries and geometric closure systems (51D20)

Cites Work

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• The double midset conjecture for continua in the plane
• Unsolved problems in geometry
• No continuum in \(E^ 2\) has the TMP. II: Triodic continua
• Subsets of \(\mathbb{R}^ n\) with convex midsets
• Equidistant Sets in Plane Triodic Continua
• Characterizing a Curve with the Double Midset Property
• Equidistant Sets and their Connectivity Properties
• An Embedding Theorem for Certain Spaces with an Equidistant Property
• Metric Characterizations of Dimension for Separable Metric Spaces
• Characterizations of metric spaces by the use of their midsets: intervals

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