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Zariski topologies on groups

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arxiv 1001.0601 v1 pith:J2MPSSHG submitted 2010-01-04 math.GR math.GN

Taras Banakh , Igor Protasov This is my paper · ORCID
classification math.GRmath.GN
keywords zariskigrouptopologydiscretecardinalityconsitingconstructedcontinuum
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abstract

The $n$-th Zariski topology on a group $G$ is generated by the sub-base consiting of the cozero sets of monomials of degree $\le n$ on $G$. We prove that for each group $G$ the 2-nd Zariski topology is not discrete and present an example of a group $G$ of cardinality continuum whose 2-nd Zariski topology has countable pseudocharacter. On the other hand, the non-topologizable group $G$ constructed by Ol'shanskii has discrete 665-th Zariski topology.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Zariski Topology on Homeomorphism groups

    math.GR 2026-01 conditional novelty 8.0 of 10

    Thompson groups F and T have Zariski topology equal to the compact-open topology, while V and Homeo(2^ω) have irreducible Zariski topology; among connected manifolds, exactly those of dimension ≤ 1 have homeomorphism ...

  2. A note on intrinsic topologies of groups

    math.GR 2025-06 conditional novelty 6.0 of 10

    The paper constructs a countable abelian group whose bounded Zariski topologies are all distinct, shows that groups with no algebraicity have hyperconnected semigroup Zariski topology, and proves that on symmetric gro...

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