| Title:
|
Partial dcpo’s and some applications (English) |
| Author:
|
Dongsheng, Zhao |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
243-260 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
directed complete poset |
| Keyword:
|
Scott topology |
| Keyword:
|
dcpo-completion |
| Keyword:
|
partial dcpo |
| Keyword:
|
C-space |
| Keyword:
|
lattice of continuous functions |
| Keyword:
|
lower semicontinuous functions |
| Keyword:
|
injective hull |
| MSC:
|
06B23 |
| MSC:
|
06B35 |
| MSC:
|
06F30 |
| MSC:
|
54A05 |
| MSC:
|
54C05 |
| MSC:
|
54C30 |
| idMR:
|
MR3007608 |
| DOI:
|
10.5817/AM2012-4-243 |
| . |
| Date available:
|
2012-12-17T13:49:17Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143099 |
| . |
| Reference:
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