The Hofmann-Mislove Theorem for general posets
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F04%3APU46315" target="_blank" >RIV/00216305:26220/04:PU46315 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—
Alternative languages
Result language
angličtina
Original language name
The Hofmann-Mislove Theorem for general posets
Original language description
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 generaalized 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.
Czech name
Hofmann-Mislovova věta pro obecné uspořádané množiny
Czech description
V této práci se snažíme nalézt co nejobecnější třídu uspořádaných množin splňující vhodně zobecněnou verzi Hofmann-Mislovovy věty.
Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
<a href="/en/project/GA201%2F03%2F0933" target="_blank" >GA201/03/0933: Set-theoretical and categorial methods in topological and algebraic structures</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2004
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models
ISBN
—
ISSN
—
e-ISSN
—
Number of pages
16
Pages from-to
1-16
Publisher name
IBFI Schloss Dagstuhl
Place of publication
Schloss Dagstuhl, Deutschland
Event location
Dagstuhl
Event date
Aug 22, 2004
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—