Rigid topologies on groups
Eli Glasner, Benjamin Weiss

TL;DR
This paper proves that every infinite, countable, residually finite group can be endowed with a Hausdorff topology that is neither discrete nor precompact, expanding understanding of possible topological structures on such groups.
Contribution
It introduces a new class of topologies on residually finite groups, demonstrating the existence of non-trivial, non-precompact Hausdorff group topologies.
Findings
Existence of non-discrete, non-precompact Hausdorff topologies on certain groups
Extension of topological group theory to residually finite groups
New insights into the structure of topologies on infinite groups
Abstract
Our main result is to show that every infinite, countable, residually finite group admits a Hausdorff group topology which is neither discrete nor precompact.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Advanced Banach Space Theory
