Details
| Original language | English |
|---|---|
| Pages (from-to) | 63-81 |
| Number of pages | 19 |
| Journal | Quaestiones mathematicae |
| Volume | 22 |
| Issue number | 1 |
| Publication status | Published - 1 Mar 1999 |
Abstract
We investigate the structure of semilattices K 0 (X) of all ordered compactifications of ordered topological spaces X with a one-point Nachbin-compactification. These semilattices and their isomorphic copies are called oc l-semilattices. We give an abstract characterization of all oc l-lattices by means of certain generalized stably continuous frames. A finite ordered set is shown to be a dual oc l-semilattice iff it is a distributive tensor, that is, a 2-consistently complete meet-semilattice T whose principal ideals are distributive and which contains two disjoint elements t o, t 1 such that s = (t o and s) V (t 1 ∧ s) for all s ∈ T. More generally, we characterize those dual oc l-semilattices which are finite unions of principal ideals.
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics (miscellaneous)
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In: Quaestiones mathematicae, Vol. 22, No. 1, 01.03.1999, p. 63-81.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Ordered onepoint-compactifications, stably continuous frames and tensors
AU - Erné, M.
AU - Reinhold, J.
PY - 1999/3/1
Y1 - 1999/3/1
N2 - We investigate the structure of semilattices K 0 (X) of all ordered compactifications of ordered topological spaces X with a one-point Nachbin-compactification. These semilattices and their isomorphic copies are called oc l-semilattices. We give an abstract characterization of all oc l-lattices by means of certain generalized stably continuous frames. A finite ordered set is shown to be a dual oc l-semilattice iff it is a distributive tensor, that is, a 2-consistently complete meet-semilattice T whose principal ideals are distributive and which contains two disjoint elements t o, t 1 such that s = (t o and s) V (t 1 ∧ s) for all s ∈ T. More generally, we characterize those dual oc l-semilattices which are finite unions of principal ideals.
AB - We investigate the structure of semilattices K 0 (X) of all ordered compactifications of ordered topological spaces X with a one-point Nachbin-compactification. These semilattices and their isomorphic copies are called oc l-semilattices. We give an abstract characterization of all oc l-lattices by means of certain generalized stably continuous frames. A finite ordered set is shown to be a dual oc l-semilattice iff it is a distributive tensor, that is, a 2-consistently complete meet-semilattice T whose principal ideals are distributive and which contains two disjoint elements t o, t 1 such that s = (t o and s) V (t 1 ∧ s) for all s ∈ T. More generally, we characterize those dual oc l-semilattices which are finite unions of principal ideals.
UR - http://www.scopus.com/inward/record.url?scp=80255133755&partnerID=8YFLogxK
U2 - 10.1080/16073606.1999.9632059
DO - 10.1080/16073606.1999.9632059
M3 - Article
AN - SCOPUS:80255133755
VL - 22
SP - 63
EP - 81
JO - Quaestiones mathematicae
JF - Quaestiones mathematicae
SN - 1607-3606
IS - 1
ER -