Partial dcpo’s and some applications

Zhao Dongsheng

Archivum Mathematicum (2012)

  • Volume: 048, Issue: 4, page 243-260
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Dongsheng, Zhao. "Partial dcpo’s and some applications." Archivum Mathematicum 048.4 (2012): 243-260. <http://eudml.org/doc/251391>.

@article{Dongsheng2012,
abstract = {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.},
author = {Dongsheng, Zhao},
journal = {Archivum Mathematicum},
keywords = {directed complete poset; Scott topology; dcpo-completion; partial dcpo; C-space; lattice of continuous functions; lower semicontinuous functions; injective hull; directed complete poset; Scott topology; dcpo-completion; partial dcpo; lattice of continuous functions; injective hull},
language = {eng},
number = {4},
pages = {243-260},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Partial dcpo’s and some applications},
url = {http://eudml.org/doc/251391},
volume = {048},
year = {2012},
}

TY - JOUR
AU - Dongsheng, Zhao
TI - Partial dcpo’s and some applications
JO - Archivum Mathematicum
PY - 2012
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 048
IS - 4
SP - 243
EP - 260
AB - 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.
LA - eng
KW - directed complete poset; Scott topology; dcpo-completion; partial dcpo; C-space; lattice of continuous functions; lower semicontinuous functions; injective hull; directed complete poset; Scott topology; dcpo-completion; partial dcpo; lattice of continuous functions; injective hull
UR - http://eudml.org/doc/251391
ER -

References

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