Comparison of Lasso and Whisker topologies on fundamental groupoids and local triviality

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Sciences, Golestan University, Gorgan, Iran

Abstract

‎This paper is devoted to comparing the Lasso topology and the Whisker topology on the fundamental groupoid. We prove that for locally path connected and semilocally simply connected spaces, the two topologies coincide. However, the converse does not hold in general, and we provide a partial converse. Furthermore, we observe that the topological fundamental groupoid is not étale, and we show that the topological fundamental groupoids of locally path connected and semilocally simply connected spaces, equipped with these topologies, are locally trivial. Through several examples, we illustrate the necessity of these conditions

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References

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Journal of Mahani Mathematical Research
Volume 15, Issue 1 - Serial Number 33
January 2026
Pages 303-315

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History

  • Receive Date: 23 March 2025
  • Revise Date: 24 July 2025
  • Accept Date: 18 August 2025

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