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Almost Polar-Dense Lattices

Published online by Cambridge University Press:  20 November 2018

R. H. Redfield
R. H. Redfield*
Affiliation:
Simon Fraser University, Burnaby, British Columbia
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Abstract

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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 255 - 261
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Birkhoff, G., Lattice Theory, third edition, Amer. Math. Soc. Coll. Pub. 25, Providence, 1967.Google Scholar
2. Bourbaki, N., General Topology, Addison-Wesley Pub. Co., Don Mills, Ontario, 1966 (translated from the French, Topologie Générale, Hermann, Paris).Google Scholar
3. Conrad, P., Lex-subgroups of lattice-ordered groups, Czech. Math. J. 18 (1968), 86-103.Google Scholar
4. Frink, O., Topology in Lattices, Trans. Amer. Math. Soc. 51 (1942), 569-582.Google Scholar
5. Redfield, R. H., A topology for a lattice-ordered group, Trans. Amer. Math. Soc. 187 (1974), 103-125.Google Scholar
6. Redfield, R. H., Generalized intervals and topology, (to appear).Google Scholar
7. Šik, F., Zur theorie der halbgeordnete Gruppen, Czech. Math. J. 6 (1956), 1-25.Google Scholar
8. Thron, W., Topological Structures, Holt, Rinehart and Winston, New York, 1966 Google Scholar