Geodesic
Almost Polar-Dense Lattices
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 255-261

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

We introduce almost polar-dense lattices and prove that the generalized interval topology of an almost polar-dense, modular lattice is equivalent to its interval topology. Furthermore, for totally ordered sets, the converse holds: if the generalized interval topology is the interval topology, then the set is almost polar-dense. 
Redfield, R. H. Almost Polar-Dense Lattices. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 255-261. doi: 10.4153/CMB-1975-049-x
@article{10_4153_CMB_1975_049_x,
     author = {Redfield, R. H.},
     title = {Almost {Polar-Dense} {Lattices}},
     journal = {Canadian mathematical bulletin},
     pages = {255--261},
     year = {1975},
     volume = {18},
     number = {2},
     doi = {10.4153/CMB-1975-049-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-049-x/}
}
TY  - JOUR
AU  - Redfield, R. H.
TI  - Almost Polar-Dense Lattices
JO  - Canadian mathematical bulletin
PY  - 1975
SP  - 255
EP  - 261
VL  - 18
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-049-x/
DO  - 10.4153/CMB-1975-049-x
ID  - 10_4153_CMB_1975_049_x
ER  - 
%0 Journal Article
%A Redfield, R. H.
%T Almost Polar-Dense Lattices
%J Canadian mathematical bulletin
%D 1975
%P 255-261
%V 18
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-049-x/
%R 10.4153/CMB-1975-049-x
%F 10_4153_CMB_1975_049_x

[1] 1. Birkhoff, G., Lattice Theory, third edition, Amer. Math. Soc. Coll. Pub. 25, Providence, 1967. Google Scholar

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

[3] 3. Conrad, P., Lex-subgroups of lattice-ordered groups, Czech. Math. J. 18 (1968), 86-103. Google Scholar

[4] 4. Frink, O., Topology in Lattices, Trans. Amer. Math. Soc. 51 (1942), 569-582. Google Scholar

[5] 5. Redfield, R. H., A topology for a lattice-ordered group, Trans. Amer. Math. Soc. 187 (1974), 103-125. Google Scholar

[6] 6. Redfield, R. H., Generalized intervals and topology, (to appear). Google Scholar

[7] 7. Šik, F., Zur theorie der halbgeordnete Gruppen, Czech. Math. J. 6 (1956), 1-25. Google Scholar

[8] 8. Thron, W., Topological Structures, Holt, Rinehart and Winston, New York, 1966 Google Scholar

Cité par Sources :