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Representing a profinite group as the homeomorphism group of a continuum

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Karl H. Hofmann, Sidney A. Morris

General Topology · Submitted 19 Aug 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is shown here that the strategy can be implemented for profinite monothetic groups $G$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1108.3876 (version 1)
Pith IDLYG264FH, Pith's permanent record of this paper and its review
CitationKarl H. Hofmann, Sidney A. Morris. "Representing a profinite group as the homeomorphism group of a continuum." arXiv:1108.3876 (2011). https://pith.science/paper/LYG264FH
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,660 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.57 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.42 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We contribute some information towards finding a general algorithm for constructing, for a given profinite group, $G$, a compact connected space, $X$, such that the full homeomorphism group, $H(X)$, with the compact-open topology is isomorphic to $G$ as a topological group. It is proposed that one should find a compact topological oriented graph $\Gamma$ such that $G\cong Aut(\Gamma)$. The replacement of the edges of $\Gamma$ by rigid continua should work as is exemplified in various instances where discrete graphs were used. It is shown here that the strategy can be implemented for profinite monothetic groups $G$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We contribute some information towards finding a general algorithm for constructing, for a given profinite group, $G$, a compact connected space, $X$, such that the full homeomorphism group, $H(X)$, with the compact-open topology is isomorphic to $G$ as a topological group. contribution 0.91 0.81 0.12 asserted 0.81
s1 It is proposed that one should find a compact topological oriented graph $\Gamma$ such that $G\cong Aut(\Gamma)$. method 0.86 0.19 0.08 hedged possibility 0.79
s2 The replacement of the edges of $\Gamma$ by rigid continua should work as is exemplified in various instances where discrete graphs were used. method 0.96 0.23 0.07 hedged possibility 0.74
s3 It is shown here that the strategy can be implemented for profinite monothetic groups $G$. result 0.84 0.92 0.76 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.62 · evidence from proof or derivation 0.93.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We contribute some information towards finding a general algorithm for constructing, for a given profinite group, $G$, a compact connected space, $X$, such that the full homeomorphism group, $H(X)$, with the compact-open topology is isomorphic to $G$ as a topological group. It is proposed that one should find a compact topological oriented graph $\Gamma$ such that $G\cong Aut(\Gamma)$. The replacement of the edges of $\Gamma$ by rigid continua should work as is exemplified in various instances where discrete graphs were used. It is shown here that the strategy can be implemented for profinite monothetic groups $G$.

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