On the topology of topological fundamental groupoids

• Pakdaman, Ali ^[1]
  1. [1] Golestan University

     Golestan University

     Irán

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 1, 2025, págs. 241-253
• Idioma: inglés
• DOI: 10.4995/agt.2025.21612
• Enlaces
  • Texto completo
• Resumen

  • ‎This paper is devoted to the Lasso and the Whisker topology of the fundamental groupoid‎. ‎We prove that topological fundamental groupoid of a given space X is locally path connected ‎in‎ ‎general‎ and is path connected if X is simply connected‎. ‎We show that for locally path connected space X‎, ‎the unit map 1 : X → π X is an embedding if and only if X is a semilocally simply connected space‎. ‎Also‎, ‎we give conditions that guarantee Hausdorffness of the topological fundamental groupoid‎.

     

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