A Graph-Theoretic Approach to the Unique Midset Property of Metric Spaces

Special Metrics

“…Theorem 3 (Ohta-Ono [28], Ito-Ohta-Ono [10]). have the UMP, where Z and Q denote the sets of the integers and rational numbers, respectively.…”

“…Theorem 4 (Ito-Ohta-Ono [10]). Let K n be the complete graph (i.e., each vertex of K n is adjacent to every other vertices) with n vertices.…”

“…Does every subspace of the real line R containing a noncompact intervals as a clopen set have the UMP? Question 4 ([10]…”