Compactification of closed preordered spaces

E. Minguzzi

Italy

Università degli Studi di Firenze

Dipartimento di Matematica Applicata "G. Sansone", Università degli Studi di Firenze, Via S. Marta 3, I-50139 Firenze, Italy

Submitted: 2013-07-29

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Accepted: 2013-07-29

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DOI: https://doi.org/10.4995/agt.2012.1630
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Keywords:

Nachbin compactification, Quasi-uniformizable space, completely regularly ordered space

Supporting agencies:

This work has been partially supported by "Gruppo Nazionale per la Fisica Matematica" (GNFM) of "Instituto Nazionale di Alta Matematica" (INDAM).

Abstract:

A topological preordered space admits a Hausdorff T2-preorder compactification if and only if it is Tychonoff and the preorder is represented by the family of continuous isotone functions. We construct the largest Hausdorff T2-preorder compactification for these spaces and clarify its relation with Nachbin’s compactification. Under local compactness the problem of the existence and identification of the smallest Hausdorff T2-preorder compactification is considered.
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