Topology on the spaces of orderings of groups. (English) Zbl 1057.06006

The author introduces a natural topology of left (right) linear orderings of an arbitrary semigroup. The set of all left orderings of a semigroup \(G\) is denoted by LO\((G)\).
Main theorem: LO\((G)\) is a compact, totally disconnected topological space.
The paper contains necessary and sufficient conditions for the fact that LO\((G)\) is homeomorphic to the Cantor set. In the second part, the author investigates the set BiO\((G)\) of all linear orderings that are both left and right orderings. Namely, he describes a new proof of the existence of universal Gröbner bases.


06F05 Ordered semigroups and monoids
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
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