Model-theoretic characterizations of arcs and simple closed curves

Bankston, Paul

doi:10.1090/S0002-9939-1988-0937843-6

Model-theoretic characterizations of arcs and simple closed curves
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by Paul Bankston

Proc. Amer. Math. Soc. 104 (1988), 898-904

DOI: https://doi.org/10.1090/S0002-9939-1988-0937843-6

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Abstract:

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.

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Taxonomies of model-theoretically defined topological properties

Model theory

Linear operators

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