Geodesic
Notes on Locally Compact Connected Topological Lattices
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1533-1536

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

I t was shown in (2) that if(1) L is a locally compact connected topological lattice and if(2) L is topologically contained in R2, the Euclidean plane, then each compact subset of L has an upper bound and a lower bound in L. I t was also asked whether this result could be proved without assuming condition (2). In this note, we show that this result continues to hold if condition (2) is weakened to: L is finite-dimensional.In (11), it was shown that the centre of a compact topological lattice is totally disconnected. We shall prove t h a t this result is also true even in a locally compact, locally convex topological lattice with 0 and 1. This yields that any locally compact topological Boolean algebra is totally disconnected. 
Choe, Tae Ho. Notes on Locally Compact Connected Topological Lattices. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1533-1536. doi: 10.4153/CJM-1969-168-x
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[1] 1. Anderson, L. W., One-dimensional topological lattices, Proc. Amer. Math. Soc. 10 (1959), 715–720. Google Scholar

[2] 2. Anderson, L. W., On the distributivity and simple connectivity of plane topological lattices, Trans. Amer. Math. Soc. 91 (1959), 102–112. Google Scholar

[3] 3. Anderson, L. W., On the breadth and co-dimension of a topological lattice, Pacific J. Math. 9 (1959), 327–333. Google Scholar

[4] 4. Anderson, L. W., The existence of continuous lattice homomorphisms, J. London Math. Soc. 87 (1962), 60–62. Google Scholar

[5] 5. Choe, T. H., On compact topological lattices of finite dimension, Trans. Amer. Math. Soc. 140 (1969), 2023–2037. Google Scholar

[6] 6. Choe, T. H., Intrinsic topologies in a topological lattice, Pacific J. Math. 28 (1969), 49–52. Google Scholar

[7] 7. Choe, T. H., The breadth and dimension of a topological lattice, Proc. Amer. Math. Soc. 23 (1969), 82–84. Google Scholar

[8] 8. Dyer, E. and Shields, A., Connectivity of topological lattices, Pacific J. Math. 9 (1959), 443–448. Google Scholar

[9] 9. Lawson, J. D., Vietoris mappings and embeddings of topological semi-lattices, Dissertation, University of Tennessee, Knoxville, Tennessee, 1967. Google Scholar

[10] 10. Lawson, J. D., Lattices with no interval homomorphisms (to appear). Google Scholar

[11] 11. Wallace, A. D., The center of a compact lattice is totally disconnected, Pacific J. Math. 7 (1957), 1237–1238. Google Scholar

[12] 12. Ward, L. W., Jr., Binary relations in topological spaces, An. Acad. Brazil. Ci. 26 (1954), 357–373. Google Scholar

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