Co-elementary Equivalence, Co-elementary Maps, and Generalized Arcs
نویسندگان
چکیده
By a generalized arc we mean a continuum with exactly two non-separating points; an 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 compacta 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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