Geodesic
Partial dcpo’s and some applications
Archivum mathematicum, Tome 48 (2012) no. 4, pp. 243-260

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces $X$, the corresponding partial dcpo’s of continuous real valued functions on $X$ are continuous partial dcpos; (iii) if a space $X$ is Hausdorff compact, the lattice of all S-lower semicontinuous functions on $X$ is the dcpo-completion of that of continuous real valued functions on the space; (iv) a topological space has an injective hull iff it is homeomorphic to the pre-Scott space of a continuous partial dcpo whose way-below relation satisfies the interpolation property.
DOI : 10.5817/AM2012-4-243
Classification : 06B23, 06B35, 06F30, 54A05, 54C05, 54C30
Keywords: directed complete poset; Scott topology; dcpo-completion; partial dcpo; C-space; lattice of continuous functions; lower semicontinuous functions; injective hull 
@article{10_5817_AM2012_4_243,
     author = {Dongsheng, Zhao},
     title = {Partial dcpo{\textquoteright}s and some applications},
     journal = {Archivum mathematicum},
     pages = {243--260},
     publisher = {mathdoc},
     volume = {48},
     number = {4},
     year = {2012},
     doi = {10.5817/AM2012-4-243},
     mrnumber = {3007608},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2012-4-243/}
}
TY  - JOUR
AU  - Dongsheng, Zhao
TI  - Partial dcpo’s and some applications
JO  - Archivum mathematicum
PY  - 2012
SP  - 243
EP  - 260
VL  - 48
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2012-4-243/
DO  - 10.5817/AM2012-4-243
LA  - en
ID  - 10_5817_AM2012_4_243
ER  - 
%0 Journal Article
%A Dongsheng, Zhao
%T Partial dcpo’s and some applications
%J Archivum mathematicum
%D 2012
%P 243-260
%V 48
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2012-4-243/
%R 10.5817/AM2012-4-243
%G en
%F 10_5817_AM2012_4_243
Dongsheng, Zhao. Partial dcpo’s and some applications. Archivum mathematicum, Tome 48 (2012) no. 4, pp. 243-260. doi: 10.5817/AM2012-4-243

Cité par Sources :