Rigid topologies on groups

Eli Glasner; Benjamin Weiss

doi:10.1016/j.topol.2024.109094

Rigid topologies on groups

Eli Glasner^*
, Benjamin Weiss

^*Corresponding author for this work

School of Mathematical Sciences

Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

Our main result is to show that every infinite, countable, residually finite group G admits a Hausdorff group topology which is neither discrete nor precompact.

Original language	English
Article number	109094
Journal	Topology and its Applications
Volume	364
DOIs	https://doi.org/10.1016/j.topol.2024.109094
State	Published - 1 Apr 2025

Keywords

Discrete topology
Precompact topology
Residually finite groups
Rigidity
Uniform rigidity

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10.1016/j.topol.2024.109094

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title = "Rigid topologies on groups",

abstract = "Our main result is to show that every infinite, countable, residually finite group G admits a Hausdorff group topology which is neither discrete nor precompact.",

keywords = "Discrete topology, Precompact topology, Residually finite groups, Rigidity, Uniform rigidity",

author = "Eli Glasner and Benjamin Weiss",

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year = "2025",

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AB - Our main result is to show that every infinite, countable, residually finite group G admits a Hausdorff group topology which is neither discrete nor precompact.

KW - Discrete topology

KW - Precompact topology

KW - Residually finite groups

KW - Rigidity

KW - Uniform rigidity

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VL - 364

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Rigid topologies on groups

Abstract

Keywords

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