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Departmental Technical Reports (CS)

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

Francisco Zapata, The University of Texas at El Paso
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-2011

Comments

Technical Report: UTEP-CS-11-16b

To appear in Studia Logica, 2012, Vol. 100, No. 1-2.

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 can be uniquely reconstructed if we know the "interior" < of the order relation. It is also known that in some cases, we can uniquely reconstruct < (and hence, topology) from the original order relation. In this paper, we show that, in general, under reasonable conditions, the open order < (and hence, the corresponding topology) can be uniquely determined from its closure.

tr11-16.pdf (126 kB)
Original file: CS-UTEP-11-16
tr11-16a.pdf (134 kB)
Revised version: CS-UTEP-11-16a

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