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Reconstructing an Open Order from Its Closure, with Applications to Space-Time Physics and to Logic

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Abstract

In his logical papers, Leo Esakia studied corresponding ordered topological spaces and order-preserving mappings. Similar spaces and mappings appear in many other application areas such the analysis of causality in space-time. It is known that under reasonable conditions, both the topology and the original order relation \({\preccurlyeq}\) can be uniquely reconstructed if we know the “interior” \({\prec}\) of the order relation. It is also known that in some cases, we can uniquely reconstruct \({\prec}\) (and hence, topology) from \({\preccurlyeq}\). In this paper, we show that, in general, under reasonable conditions, the open order \({\prec}\) (and hence, the corresponding topology) can be uniquely determined from its closure \({\preccurlyeq}\).

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Authors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX, 79968, USA

    Francisco Zapata & Vladik Kreinovich

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  1. Francisco Zapata
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  2. Vladik Kreinovich
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Correspondence to Vladik Kreinovich.

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In memoriam Leo Esakia

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Zapata, F., Kreinovich, V. Reconstructing an Open Order from Its Closure, with Applications to Space-Time Physics and to Logic. Stud Logica 100, 419–435 (2012). https://doi.org/10.1007/s11225-012-9386-y

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