2025/06/12 by Frédéric Mynard, Mynard, Frédéric · 1 citation
Decision Sciences · Mathematics · #18F99 #54A20 #Algebraic and Geometric Analysis #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2506.10951
openalex publication_date 2025/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this note is to illustrate a parallel between (pre)topologies when seen among convergence spaces and (pre)approach spaces when seen among convergence approach spaces, that appears to be a more complete parallel than in the traditional presentation of these approach structures. This sheds some light on the reflector from the category of convergence approach spaces to that of approach spaces and even on the structure of approach spaces as such. This point of view allows for a characterization of approach spaces among convergence approach spaces represented as pointfree convergence frames as in [18].