Year: 2010
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Banakh, Taras, Protasov, Igor
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1650468149