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

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

1994-08-10

arxiv.org/abs/math/9408203v1

Mathematics

Logic

Scientific paper

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 $f:X \to Y$ 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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