Geodesic
Connectedness Properties of Lattices
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 314-320

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DOI

Let L be a lattice and q a convergence structure (or a topology) finer than the interval topology of L. In case of compact maximal chains and continuous lattice translations, the connected components of the space (L,q) are characterized using lattice conditions only. Moreover, lattice conditions of L are related to connectedness conditions of the order convergence space (L, o). Throughout this note, maximal chain conditions and maximal chain techniques play an important role.
DOI : 10.4153/CMB-1986-048-2
Mots-clés : 54A20, 54D05, 54H12, Maximal chains in lattices, convergence structures (topologies) on lattices, order convergence, interval topology, connected components 
Vainio, R. Connectedness Properties of Lattices. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 314-320. doi: 10.4153/CMB-1986-048-2
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     author = {Vainio, R.},
     title = {Connectedness {Properties} of {Lattices}},
     journal = {Canadian mathematical bulletin},
     pages = {314--320},
     year = {1986},
     volume = {29},
     number = {3},
     doi = {10.4153/CMB-1986-048-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-048-2/}
}
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