License
When quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-1199
URL: http://drops.dagstuhl.de/opus/volltexte/2005/119/
Go to the corresponding Portal


Kovar, Martin

The Hofmann-Mislove Theorem for general posets

pdf-format:
Document 1.pdf (253 KB)


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:DSP:2005:119,
  author =	{Martin Kovar},
  title =	{The Hofmann-Mislove Theorem for general posets},
  booktitle =	{Spatial Representation: Discrete vs. Continuous Computational Models},
  year =	{2005},
  editor =	{Ralph Kopperman and Michael B. Smyth and Dieter Spreen and Julian Webster},
  number =	{04351},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2005/119},
  annote =	{Keywords: Posets , generalized Scott topology , Scott open filters , (filtered) compactness , saturated}
}

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


DROPS-Home | Fulltext Search | Imprint Published by LZI