2025/04/07 by Pedro J. Chocano, Chocano, Pedro J.
Computer Science · Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2504.05175
openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study flows and semiflows defined on any given finite topological T0-space X. We show that there exist non-trivial semiflows on X, unless X is a minimal finite space. Specifically, non-trivial semiflows exist if and only if X contains down beat points, and a non-trivial semiflow is essentially a strong deformation retraction. As a consequence of this result, we provide a new and concise proof that the only flow that can be defined on X is the trivial flow. Finally, we discuss the number of different semiflows that can be defined on X in terms of down beat points and other special points.