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Co-elementary equivalence, co-elementary maps, and generalized arcs

1994/08/10 by Paul Bankston, Bankston, Paul
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.math/9408203

arxiv created 1994/08/10 · openalex publication_date 1994/08/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By a \bf generalized arc\/ we mean a continuum with exactly two non-separating points; an \bf arc is a metrizable generalized arc. It is well known that any two arcs are homeomorphic (to the real closed unit interval); we show that any two generalized arcs are co-elementarily equivalent, and that co-elementary images of generalized arcs are generalized arcs. We also show that if f:X → Y is a function between compact Hausdorff spaces and if X is an arc, then f is a co-elementary map if and only if Y is an arc and f is a monotone continuous surjection.

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