Geodesic
Topologies of Lattice Products
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1004-1014

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

A number of different ways of defining topologies in a lattice or partially ordered set in terms of the order relation are known. Three of these methods have proved to be useful and convenient for lattices of special types, namely the ideal topology, the interval topology, and the new interval topology of Garrett Birkhoff. In another paper (2) we have shown that these three topologies are equivalent for chains (totally ordered sets), where they reduce to the usual intrinsic topology of the chain.Since many important lattices are either direct products of chains or sublattices of such products, it is natural to ask what relationships exist between the various order topologies of a direct product of lattices and those of the lattices themselves. 
Alo, Richard A.; Frink, Orrin. Topologies of Lattice Products. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1004-1014. doi: 10.4153/CJM-1966-101-2
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