Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 217-243 |
| Seitenumfang | 27 |
| Fachzeitschrift | Applied categorical structures |
| Jahrgang | 9 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - Mai 2001 |
Abstract
The core of a point in a topological space is the intersection of its neighborhoods. We construct certain completions and compactifications for densely core-generated spaces, i.e., T0-spaces having a subbasis of open cores such that the points with open cores are dense in the associated patch space. All T0-spaces with a minimal basis are in that class. Densely core-generated spaces admit not only a coarsest quasi-uniformity (the unique totally bounded transitive compatible quasi-uniformity), but also a purely order-theoretical description by means of their specialization order and a suitable join-dense subset (join-basis). It turns out that the underlying ordered sets of the completions and compactifications obtained are, up to isomorphism, certain ideal completions of the join-basis. The topology of the resulting completion or compactification is the Lawson topology or the Scott topology, or a slight modification of these.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Theoretische Informatik
- Informatik (insg.)
- Allgemeine Computerwissenschaft
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in: Applied categorical structures, Jahrgang 9, Nr. 3, 05.2001, S. 217-243.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Ideal completions and compactifications
AU - Erné, Marcel
PY - 2001/5
Y1 - 2001/5
N2 - The core of a point in a topological space is the intersection of its neighborhoods. We construct certain completions and compactifications for densely core-generated spaces, i.e., T0-spaces having a subbasis of open cores such that the points with open cores are dense in the associated patch space. All T0-spaces with a minimal basis are in that class. Densely core-generated spaces admit not only a coarsest quasi-uniformity (the unique totally bounded transitive compatible quasi-uniformity), but also a purely order-theoretical description by means of their specialization order and a suitable join-dense subset (join-basis). It turns out that the underlying ordered sets of the completions and compactifications obtained are, up to isomorphism, certain ideal completions of the join-basis. The topology of the resulting completion or compactification is the Lawson topology or the Scott topology, or a slight modification of these.
AB - The core of a point in a topological space is the intersection of its neighborhoods. We construct certain completions and compactifications for densely core-generated spaces, i.e., T0-spaces having a subbasis of open cores such that the points with open cores are dense in the associated patch space. All T0-spaces with a minimal basis are in that class. Densely core-generated spaces admit not only a coarsest quasi-uniformity (the unique totally bounded transitive compatible quasi-uniformity), but also a purely order-theoretical description by means of their specialization order and a suitable join-dense subset (join-basis). It turns out that the underlying ordered sets of the completions and compactifications obtained are, up to isomorphism, certain ideal completions of the join-basis. The topology of the resulting completion or compactification is the Lawson topology or the Scott topology, or a slight modification of these.
KW - (Ordered) topological space
KW - (Quasi-)uniform space
KW - (Strongly) sober
KW - Cauchy filter
KW - Compactification
KW - Completion
KW - Core
KW - Ideal
KW - Totally (order-) separated
UR - http://www.scopus.com/inward/record.url?scp=0035331085&partnerID=8YFLogxK
U2 - 10.1023/A:1011260817824
DO - 10.1023/A:1011260817824
M3 - Article
AN - SCOPUS:0035331085
VL - 9
SP - 217
EP - 243
JO - Applied categorical structures
JF - Applied categorical structures
SN - 0927-2852
IS - 3
ER -