Format of Original
American Mathematical Society
Proceedings of the American Mathematical Society
Original Item ID
doi: 10.1090/S0002-9939-1988-0937843-6; Shelves: QA1 .A5215 Storage S
Two compact Hausdorff spaces are co-elementarily equivalent if they have homeomorphic ultracopowers; equivalently if their Banach spaces of continuous real-valued functions have isometrically isomorphic Banach ultrapowers (or, approximately satisfy the same positive-bounded sentences). We prove here that any locally connected compact metrizable space co-elementarily equivalent with an arc (resp. a simple closed curve) is itself an arc (resp. a simple closed curve). The hypotheses of metrizability and local connectedness cannot be dropped.
Bankston, Paul, "Model-theoretic Characterizations of Arcs and Simple Closed Curves" (1988). Mathematics, Statistics and Computer Science Faculty Research and Publications. 133.