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Open maps of toposes

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Abstract

We present a concept of “openness” for geometric morphisms between toposes, which extends the usual notion of “open map of spaces”, and investigate some of its properties. Our two main results are that open maps are precisely those whose inverse image functors preserve full first-order logic, and that open maps and open surjections are stable under bounded pullback in Top. These two results extend earlier work of C. J. Mikkelsen [11] and M. Coste [3] respectively; they are also closely related to recent work of A. Joyal and M. Tierney [9].

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  1. Department of Pure Mathematics, University of Cambridge, 16 Mill Lane, CB2 1SB, Cambridge, England

    Peter T. Johnstone

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  1. Peter T. Johnstone
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Johnstone, P.T. Open maps of toposes. Manuscripta Math 31, 217–247 (1980). https://doi.org/10.1007/BF01303275

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  • DOI: https://doi.org/10.1007/BF01303275

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