License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.04351.20
URN: urn:nbn:de:0030-drops-1199
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2005/119/
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Kovar, Martin

The Hofmann-Mislove Theorem for general posets

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04351.KovarMartin3.Paper.119.pdf (0.2 MB)

Abstract

In this paper we attempt to find and investigate the most general class of posets which satisfy a properly generalized version of the Hofmann-Mislove theorem. For that purpose, we generalize and study some notions (like compactness, the Scott topology, Scott open filters, prime elements, the spectrum etc.), and adjust them for use in general posets. Then we characterize the posets satisfying the Hofmann-Mislove theorem by the relationship between the generalized Scott closed prime subsets and the generalized prime elements of the poset. The theory become classic for distributive lattices. Remark that the topologies induced on the generalized spectra in general need not be
sober.

BibTeX - Entry

@InProceedings{kovar:DagSemProc.04351.20,
  author =	{Kovar, Martin},
  title =	{{The Hofmann-Mislove Theorem for general posets}},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{4351},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2005/119},
  URN =		{urn:nbn:de:0030-drops-1199},
  doi =		{10.4230/DagSemProc.04351.20},
  annote =	{Keywords: Posets , generalized Scott topology , Scott open filters , (filtered) compactness , saturated}
}

Keywords: Posets , generalized Scott topology , Scott open filters , (filtered) compactness , saturated
Collection: 04351 - Spatial Representation: Discrete vs. Continuous Computational Models
Issue Date: 2005
Date of publication: 22.04.2005

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