1985/11/01 by L. Foged · 31 citations
Mathematics · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Homotopy and Cohomology in Algebraic Topology #Annotation #Algorithm #Semantics (computer science) #Metric (unit) #Computer science #Type (biology) #Metric space #Closure (psychology) #Space (punctuation) #Artificial intelligence #Mathematics #Discrete mathematics #Programming language #Biology
paper · pdf · doi:10.1090/s0002-9939-1985-0806093-3
published in Proceedings of the American Mathematical Society 95(3), 487-490 (American Mathematical Society)
openalex publication_date 1985/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/10
We prove that a regular topological space is the image of a metric space under a closed mapping if and only if it is a Fréchet space with a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma"> <mml:semantics> <mml:mi> σ </mml:mi> <mml:annotation encoding="application/x-tex">σ</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -hereditarily closure-preserving <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding="application/x-tex">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -network.