Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Model-theoretic characterizations of arcs and simple closed curves


Author: Paul Bankston
Journal: Proc. Amer. Math. Soc. 104 (1988), 898-904
MSC: Primary 03C20; Secondary 03C65, 54B25, 54D05, 54D35, 54F25, 54F65
MathSciNet review: 937843
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03C20, 03C65, 54B25, 54D05, 54D35, 54F25, 54F65

Retrieve articles in all journals with MSC: 03C20, 03C65, 54B25, 54D05, 54D35, 54F25, 54F65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0937843-6
Keywords: co-elementary equivalence, compact Hausdorff spaces, Peano continua, ultracoproducts, arcs, simple closed curves
Article copyright: © Copyright 1988 American Mathematical Society