2024/07/03 by Yoshito Ishiki, Ishiki, Yoshito
Engineering · #Control and Dynamics of Mobile Robots #FOS: Mathematics #General Topology (math.GN) #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2407.03030
openalex publication_date 2024/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, for a metrizable space Z, we consider the space of metrics that generate the same topology of Z, and that space of metrics is equipped with the supremum metrics. For a metrizable space X and a closed subset A of it, we construct a map E from the space of metrics on A into the space of metrics on X such that E is an extension of metrics and preserves the supremum metrics between metrics.