2021/01/12 by Brendon LaBuz, LaBuz, Brendon · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #General Mathematics (math.GM) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2101.07656
openalex publication_date 2021/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Brodskiy, Dydak, LaBuz, and Mitra introduced the concepts of uniform joinability and local uniform joinability for uniform spaces when developing their theory of generalized uniform covering maps which was motivated by a paper by Berestovskii and Plaut. (Local) uniform joinability can be thought of as analogous to (local) path connectedness. A chain connected locally uniformly joinable uniform space is uniformly joinable. This note gives an example of a metric space that is uniformly joinable but not locally uniformly joinable. Plaut recently defined the concept of a weakly chained uniform space. We show that a weakly chained metrizable uniform space is locally uniformly joinable. Since local uniform joinability is equivalent to pointed 1-movability for metric continua, we find that weak chainability is equivalent to pointed 1-movability for such spaces.