Zariski topologies on groups

2010/01/04 by Тарас Банах, Banakh, Taras, Ігор Протасов +1 · 1 citation
Mathematics · Computer Science · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.1001.0601

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 ≤ 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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