Detail publikačního výsledku

The Hofmann-Mislove Theorem for general posets

KOVÁR, M.

Originální název

The Hofmann-Mislove Theorem for general posets

Anglický název

The Hofmann-Mislove Theorem for general posets

Druh

Stať ve sborníku v databázi WoS či Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova v angličtině

Posets, generalized Scott topology, Scott open filters, (filtered) compactness, saturated sets, prime elements, prime subsets

Autoři

KOVÁR, M.

Rok RIV

2011

Vydáno

14.10.2004

Nakladatel

IBFI Schloss Dagstuhl

Místo

Schloss Dagstuhl, Deutschland

Kniha

Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models

Svazek

1

Číslo

04351

Strany od

1

Strany počet

16

URL

ftp://ftp.dagstuhl.de/pub/Proceedings/04/04351/04351.KovarMartin3.Paper!.pdf

BibTex

@inproceedings{BUT11709,
  author="Martin {Kovár}",
  title="The Hofmann-Mislove Theorem for general posets",
  booktitle="Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models",
  year="2004",
  volume="1",
  number="04351",
  pages="16",
  publisher="IBFI  Schloss Dagstuhl",
  address="Schloss Dagstuhl, Deutschland",
  url="ftp://ftp.dagstuhl.de/pub/Proceedings/04/04351/04351.KovarMartin3.Paper!.pdf"
}