Geodesic
Lattices of extensions of cyclically ordered sets and compactifications of generalized cyclically ordered spaces
Matematičeskie zametki, Tome 116 (2024) no. 4, pp. 599-613

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The notion of an extension and a completion of a cyclically ordered set is introduced. It is shown that the family of all extensions of a cyclically ordered set has the structure of a complete lattice. Completions, which are cyclically ordered compactifications of generalized cyclically ordered spaces, are complete sublattices of this lattice.
Keywords: cyclic order, ordered space, extension, completion, lattice compactification. 
G. B. Sorin. Lattices of extensions of cyclically ordered sets and compactifications of generalized cyclically ordered spaces. Matematičeskie zametki, Tome 116 (2024) no. 4, pp. 599-613. http://geodesic.mathdoc.fr/item/MZM_2024_116_4_a8/
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