On Topologized Fundamental Groups with Small Loop Transfer Viewpoints


In this paper, by introducing some kind of small loop transfer spaces at a point, we study the behavior of topologized fundamental groups with the compact-open topology and the whisker topology, \(\pi _{1}^{qtop}(X,x_{0})\) and \(\pi _{1}^{wh}(X,x_{0})\), respectively. In particular, we give necessary or sufficient conditions for equality and being topological group of these two topologized fundamental groups. Finally, we give some examples to show that the converse of some of these implications do not hold, in general.

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The authors would like to thank the referee for the valuable comments and suggestions that helped to improve the manuscript.


This research was supported by a grant from Ferdowsi University of Mashhad-Graduate Studies (No. 38590).

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Correspondence to Behrooz Mashayekhy.

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Jamali, N., Mashayekhy, B., Torabi, H. et al. On Topologized Fundamental Groups with Small Loop Transfer Viewpoints. Acta Math Vietnam 44, 711–722 (2019). https://doi.org/10.1007/s40306-018-0264-1

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  • Small loop transfer space
  • Quasitopological fundamental group
  • Whisker topology
  • Topological group

Mathematics Subject Classification (2010)

  • 57M05
  • 57M12
  • 55P35
  • 54H11