Geodesic
Ordering Uniform Completions of Partially Ordered Sets
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 644-664

Voir la notice de l'article provenant de la source Cambridge University Press

Let (P, ) be a (nearly) uniform ordered space. Let (P, ) be the uniform completion of (P, ) at . Several partial orders for P are introduced and discussed. One of these orders provides an adjoint to the functor which embeds the category of uniformly complete uniform ordered spaces in the category of uniform ordered spaces, both categories with uniformly continuous order-preserving functions. When P is a join-semilattice with uniformly continuous join, two of these orders coalesce to the unique partial order with respect to which P is a join-semilattice, P is a join-subsemilattice of P, and the join on P is continuous. 
Redfield, R. H. Ordering Uniform Completions of Partially Ordered Sets. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 644-664. doi: 10.4153/CJM-1974-062-4
@article{10_4153_CJM_1974_062_4,
     author = {Redfield, R. H.},
     title = {Ordering {Uniform} {Completions} of {Partially} {Ordered} {Sets}},
     journal = {Canadian journal of mathematics},
     pages = {644--664},
     year = {1974},
     volume = {26},
     number = {3},
     doi = {10.4153/CJM-1974-062-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-062-4/}
}
TY  - JOUR
AU  - Redfield, R. H.
TI  - Ordering Uniform Completions of Partially Ordered Sets
JO  - Canadian journal of mathematics
PY  - 1974
SP  - 644
EP  - 664
VL  - 26
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-062-4/
DO  - 10.4153/CJM-1974-062-4
ID  - 10_4153_CJM_1974_062_4
ER  - 
%0 Journal Article
%A Redfield, R. H.
%T Ordering Uniform Completions of Partially Ordered Sets
%J Canadian journal of mathematics
%D 1974
%P 644-664
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1974-062-4/
%R 10.4153/CJM-1974-062-4
%F 10_4153_CJM_1974_062_4

[1] 1. Birkhoff, G., Lattice theory, 3rd. edition (Amer. Math. Soc. Colloquium Pub. 25, Providence, 1967). Google Scholar

[2] 2. Birkhoff, G. and MacLane, S., Algebra (MacMillan Co., New York, 1967). Google Scholar

[3] 3. Bourbaki, N., General topology (Addison-Wesley Pub. Co., Don Mills, Ontario, 1966). (translated from the French, Hermann, Paris.) Google Scholar

[4] 4. Conrad, P., The topological completion and the linearly compact hull of an abelian l-group (to appear). Google Scholar

[5] 5. Kiseleva, T. G., Partially ordered sets endowed with a uniform structure (Russian), Vestnik Leningrad. Univ. 22 (1967), no. 13, 51–57. Google Scholar

[6] 6. Nachbin, L., Topology and order (D. Van Nostrand Company, Inc., Princeton, 1965). Google Scholar

[7] 7. Thron, W., Topological structures (Holt, Rinehart and Winston, New York, 1966). Google Scholar

Cité par Sources :