Document Type

Conference Proceeding

Language

eng

Format of Original

7 p.

Publication Date

11-1988

Publisher

American Mathematical Society

Source Publication

Proceedings of the American Mathematical Society

Source ISSN

0002-9939

Original Item ID

doi: 10.1090/S0002-9939-1988-0937843-6; Shelves: QA1 .A5215 Storage S

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.

Comments

Published version. Proceedings of the American Mathematical Society, Vol. 104, No. 3 (November 1988): 898-904. DOI. © American Mathematical Society 1988. Used with permission.

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