Format of Original
American Mathematical Society
Proceedings of the American Mathematical Society
Original Item ID
doi: 10.1090/S0002-9939-97-04088-4; Shelves: QA1 .A5215 Storage S
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.
Bankston, Paul, "Co-elementary Equivalence, Co-elementary Maps, and Generalized Arcs" (1997). Mathematics, Statistics and Computer Science Faculty Research and Publications. 137.